http://www.physicsbook.gatech.edu/api.php?action=feedcontributions&feedformat=atom&user=Nvohra3Physics Book - User contributions [en]2026-05-02T03:42:53ZUser contributionsMediaWiki 1.42.7http://www.physicsbook.gatech.edu/index.php?title=Systems_with_Nonzero_Torque&diff=20374Systems with Nonzero Torque2015-12-08T04:15:46Z<p>Nvohra3: /* References */</p>
<hr />
<div>In certain systems, external torques have an effect on a system's angular momentum. Since these external forces do not sum to zero, we end up with a system with non-zero net torque.<br />
<br />
==The Main Idea==<br />
<br />
With previous systems involving torque, we've been fortunate enough to have systems where the net torque is non-zero, hence <math> \vec{L}_{final} = \vec{L}_{initial}. </math> <br><br />
See systems with zero net torque in "See Also" section below for more information. <br><br />
<br />
However, we're not always fortunate enough to have such systems. In such cases, our computations become a little more complicated, and we'll see how below.<br />
<br />
===A Mathematical Model===<br />
<br />
The angular momentum principle is the following: <math>{\frac{d\vec{L}}{dt}}= \vec{r} * \vec{F}_{net} = \vec{т}_{net} </math> <br><br />
As previously mentioned, we'll now look at the case where <math> \vec{F}_{net} </math> is NOT equal to 0.<br />
<br />
===How to Model in VPython===<br />
The following code should be self explanatory and can be used as a template for modeling a system involving torque.<br />
Important things to note are the use of cross() to calculate the cross product between two vectors and sphere.rotate() to rotate a sphere object around some axis at some angle.<br />
# -*- coding: utf-8 -*-<br />
from __future__ import division<br />
from visual import *<br />
<br />
NUM_LOOP_ITERATIONS = 5000 # Arbitrarily chose 5000<br />
wheel = sphere(pos = vector(0, 0, 0), radius = 10, color = color.cyan, mass = 5)<br />
axisOfRotation = vector(5, 0, 0) # Axis of rotation of system<br />
force = vector(5, 0, 0) # Force acting on system<br />
delta_t = 1<br />
t = 0<br />
angularMomentum= vector(20, 0, 0) # Initial angular momentum<br />
omega = 40 # Initial angular speed<br />
inertia = (wheel.mass * wheel.radius ** 2)/12 # Calculating intertia; ML^2 / 12<br />
dtheta = 0<br />
while t < 5000:<br />
rate(500)<br />
torque = cross(wheel.pos, force) # torque = position x force<br />
angularMomentum += torque * delta_t # Update angular momentum<br />
omega = angularMomentum / inertia<br />
omegaScalar = dot(omega, norm(axisOfRotation))<br />
dtheta += omegaScalar * delta_t<br />
wheel.rotate(angle=dtheta, axis = axisOfRotation, origin = wheel.pos)<br />
t += delta_t<br />
<br />
==Examples==<br />
===Simple===<br />
If a constant net torque (non-zero) is exerted on an object, which of the following quantities cannot be constant? <br><br />
A) Moment of inertia <br><br />
B) Center of mass <br><br />
C) Angular momentum <br><br />
D) Angular velocity <br><br />
E) Angular acceleration <br><br />
<br><br />
Solution/Explanation: <br><br />
C, D. Why? <br><br />
A) Moment of inertia does not change depending on whether torque is exerted on an object; moment of inertia depends on the object and axis of rotation, nothing more. <br><br />
B) Center of mass doesn't change with applied torque as well. <br><br />
C) Angular momentum is equal to inertia times angular speed, and we establish below that angular velocity changes. <br><br />
D) Angular velocity changes since a constant force is being applied to the object, so it's speed/velocity must inherently increase. <br><br />
E) Because the torque being applied is constant, angular acceleration does not change (remember, acceleration is a measure of the rate of change of velocity!). <br><br />
<br />
===Middling===<br />
<br />
[[File:ProblemAndSolution.jpg]]<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
:::I had taken physics in high school, and a majority of the concepts covered in this class were familiar to me. However, I had never seen any of the material we covered in the last unit (like angular momentum, conservation of angular momentum, torque, etc.). This material was new and something I found interesting since it went a step further with the information we learned throughout the semester.<br />
[[File:HaloGameplay.jpg|420px|thumb|right|Example of physics being used to model the motion of vehicles in Halo 2]]<br />
#How is it connected to your major? Is there an interesting industrial application?<br />
:::My major is Computer Science, so I cannot really draw a clear line between my current coursework and this topic. That being said, physics is, of course, used in computer science. A good example would be in programming games where most interactions between objects involve physics of some kind, and the programmers/game designers want to model realistic situations in game. <br><br />
:::Another example that never really dawned upon me until about halfway through the semester was that both topics require a decent level skill in problem solving/reasoning. I've liked physics this semester because (and I guess this just applies to math in general) it's almost beautiful just to see how, in the end, everything works out and makes sense. Throughout the semester, I've never had a moment during class where I've flat out said, "No, that doesn't make sense" simply because that's never happened. I've never been a huge fan of physics, but even I can appreciate something that comes together so well.<br />
<br />
==History==<br />
<br />
This concept doesn't have it's own history since it's just a section under torque, so refer to http://www.physicsbook.gatech.edu/Torque#History for more information.<br />
<br />
== See also ==<br />
<br />
A general description of torque:<br />
http://www.physicsbook.gatech.edu/Torque<br />
<br />
===External links===<br />
[https://www.youtube.com/watch?v=mvzSjRFQbHE A brief overview on systems with non-zero torque]<br />
<br />
==References==<br />
<br />
Matters and Interactions: 4th Edition <br><br />
[https://drive.google.com/file/d/0B6hjEAwn8lB-WURaNmRvVGFjUnM/edit College Physics: Ninth Edition] <br><br />
[[Category:Angular Momentum]]</div>Nvohra3http://www.physicsbook.gatech.edu/index.php?title=Systems_with_Nonzero_Torque&diff=20373Systems with Nonzero Torque2015-12-08T04:15:28Z<p>Nvohra3: /* References */</p>
<hr />
<div>In certain systems, external torques have an effect on a system's angular momentum. Since these external forces do not sum to zero, we end up with a system with non-zero net torque.<br />
<br />
==The Main Idea==<br />
<br />
With previous systems involving torque, we've been fortunate enough to have systems where the net torque is non-zero, hence <math> \vec{L}_{final} = \vec{L}_{initial}. </math> <br><br />
See systems with zero net torque in "See Also" section below for more information. <br><br />
<br />
However, we're not always fortunate enough to have such systems. In such cases, our computations become a little more complicated, and we'll see how below.<br />
<br />
===A Mathematical Model===<br />
<br />
The angular momentum principle is the following: <math>{\frac{d\vec{L}}{dt}}= \vec{r} * \vec{F}_{net} = \vec{т}_{net} </math> <br><br />
As previously mentioned, we'll now look at the case where <math> \vec{F}_{net} </math> is NOT equal to 0.<br />
<br />
===How to Model in VPython===<br />
The following code should be self explanatory and can be used as a template for modeling a system involving torque.<br />
Important things to note are the use of cross() to calculate the cross product between two vectors and sphere.rotate() to rotate a sphere object around some axis at some angle.<br />
# -*- coding: utf-8 -*-<br />
from __future__ import division<br />
from visual import *<br />
<br />
NUM_LOOP_ITERATIONS = 5000 # Arbitrarily chose 5000<br />
wheel = sphere(pos = vector(0, 0, 0), radius = 10, color = color.cyan, mass = 5)<br />
axisOfRotation = vector(5, 0, 0) # Axis of rotation of system<br />
force = vector(5, 0, 0) # Force acting on system<br />
delta_t = 1<br />
t = 0<br />
angularMomentum= vector(20, 0, 0) # Initial angular momentum<br />
omega = 40 # Initial angular speed<br />
inertia = (wheel.mass * wheel.radius ** 2)/12 # Calculating intertia; ML^2 / 12<br />
dtheta = 0<br />
while t < 5000:<br />
rate(500)<br />
torque = cross(wheel.pos, force) # torque = position x force<br />
angularMomentum += torque * delta_t # Update angular momentum<br />
omega = angularMomentum / inertia<br />
omegaScalar = dot(omega, norm(axisOfRotation))<br />
dtheta += omegaScalar * delta_t<br />
wheel.rotate(angle=dtheta, axis = axisOfRotation, origin = wheel.pos)<br />
t += delta_t<br />
<br />
==Examples==<br />
===Simple===<br />
If a constant net torque (non-zero) is exerted on an object, which of the following quantities cannot be constant? <br><br />
A) Moment of inertia <br><br />
B) Center of mass <br><br />
C) Angular momentum <br><br />
D) Angular velocity <br><br />
E) Angular acceleration <br><br />
<br><br />
Solution/Explanation: <br><br />
C, D. Why? <br><br />
A) Moment of inertia does not change depending on whether torque is exerted on an object; moment of inertia depends on the object and axis of rotation, nothing more. <br><br />
B) Center of mass doesn't change with applied torque as well. <br><br />
C) Angular momentum is equal to inertia times angular speed, and we establish below that angular velocity changes. <br><br />
D) Angular velocity changes since a constant force is being applied to the object, so it's speed/velocity must inherently increase. <br><br />
E) Because the torque being applied is constant, angular acceleration does not change (remember, acceleration is a measure of the rate of change of velocity!). <br><br />
<br />
===Middling===<br />
<br />
[[File:ProblemAndSolution.jpg]]<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
:::I had taken physics in high school, and a majority of the concepts covered in this class were familiar to me. However, I had never seen any of the material we covered in the last unit (like angular momentum, conservation of angular momentum, torque, etc.). This material was new and something I found interesting since it went a step further with the information we learned throughout the semester.<br />
[[File:HaloGameplay.jpg|420px|thumb|right|Example of physics being used to model the motion of vehicles in Halo 2]]<br />
#How is it connected to your major? Is there an interesting industrial application?<br />
:::My major is Computer Science, so I cannot really draw a clear line between my current coursework and this topic. That being said, physics is, of course, used in computer science. A good example would be in programming games where most interactions between objects involve physics of some kind, and the programmers/game designers want to model realistic situations in game. <br><br />
:::Another example that never really dawned upon me until about halfway through the semester was that both topics require a decent level skill in problem solving/reasoning. I've liked physics this semester because (and I guess this just applies to math in general) it's almost beautiful just to see how, in the end, everything works out and makes sense. Throughout the semester, I've never had a moment during class where I've flat out said, "No, that doesn't make sense" simply because that's never happened. I've never been a huge fan of physics, but even I can appreciate something that comes together so well.<br />
<br />
==History==<br />
<br />
This concept doesn't have it's own history since it's just a section under torque, so refer to http://www.physicsbook.gatech.edu/Torque#History for more information.<br />
<br />
== See also ==<br />
<br />
A general description of torque:<br />
http://www.physicsbook.gatech.edu/Torque<br />
<br />
===External links===<br />
[https://www.youtube.com/watch?v=mvzSjRFQbHE A brief overview on systems with non-zero torque]<br />
<br />
==References==<br />
<br />
Matters and Interactions: 4th Edition <br><br />
WebAssign <br><br />
[ https://drive.google.com/file/d/0B6hjEAwn8lB-WURaNmRvVGFjUnM/edit College Physics: Ninth Edition] <br><br />
[[Category:Angular Momentum]]</div>Nvohra3http://www.physicsbook.gatech.edu/index.php?title=Systems_with_Nonzero_Torque&diff=20372Systems with Nonzero Torque2015-12-08T04:12:16Z<p>Nvohra3: /* Connectedness */</p>
<hr />
<div>In certain systems, external torques have an effect on a system's angular momentum. Since these external forces do not sum to zero, we end up with a system with non-zero net torque.<br />
<br />
==The Main Idea==<br />
<br />
With previous systems involving torque, we've been fortunate enough to have systems where the net torque is non-zero, hence <math> \vec{L}_{final} = \vec{L}_{initial}. </math> <br><br />
See systems with zero net torque in "See Also" section below for more information. <br><br />
<br />
However, we're not always fortunate enough to have such systems. In such cases, our computations become a little more complicated, and we'll see how below.<br />
<br />
===A Mathematical Model===<br />
<br />
The angular momentum principle is the following: <math>{\frac{d\vec{L}}{dt}}= \vec{r} * \vec{F}_{net} = \vec{т}_{net} </math> <br><br />
As previously mentioned, we'll now look at the case where <math> \vec{F}_{net} </math> is NOT equal to 0.<br />
<br />
===How to Model in VPython===<br />
The following code should be self explanatory and can be used as a template for modeling a system involving torque.<br />
Important things to note are the use of cross() to calculate the cross product between two vectors and sphere.rotate() to rotate a sphere object around some axis at some angle.<br />
# -*- coding: utf-8 -*-<br />
from __future__ import division<br />
from visual import *<br />
<br />
NUM_LOOP_ITERATIONS = 5000 # Arbitrarily chose 5000<br />
wheel = sphere(pos = vector(0, 0, 0), radius = 10, color = color.cyan, mass = 5)<br />
axisOfRotation = vector(5, 0, 0) # Axis of rotation of system<br />
force = vector(5, 0, 0) # Force acting on system<br />
delta_t = 1<br />
t = 0<br />
angularMomentum= vector(20, 0, 0) # Initial angular momentum<br />
omega = 40 # Initial angular speed<br />
inertia = (wheel.mass * wheel.radius ** 2)/12 # Calculating intertia; ML^2 / 12<br />
dtheta = 0<br />
while t < 5000:<br />
rate(500)<br />
torque = cross(wheel.pos, force) # torque = position x force<br />
angularMomentum += torque * delta_t # Update angular momentum<br />
omega = angularMomentum / inertia<br />
omegaScalar = dot(omega, norm(axisOfRotation))<br />
dtheta += omegaScalar * delta_t<br />
wheel.rotate(angle=dtheta, axis = axisOfRotation, origin = wheel.pos)<br />
t += delta_t<br />
<br />
==Examples==<br />
===Simple===<br />
If a constant net torque (non-zero) is exerted on an object, which of the following quantities cannot be constant? <br><br />
A) Moment of inertia <br><br />
B) Center of mass <br><br />
C) Angular momentum <br><br />
D) Angular velocity <br><br />
E) Angular acceleration <br><br />
<br><br />
Solution/Explanation: <br><br />
C, D. Why? <br><br />
A) Moment of inertia does not change depending on whether torque is exerted on an object; moment of inertia depends on the object and axis of rotation, nothing more. <br><br />
B) Center of mass doesn't change with applied torque as well. <br><br />
C) Angular momentum is equal to inertia times angular speed, and we establish below that angular velocity changes. <br><br />
D) Angular velocity changes since a constant force is being applied to the object, so it's speed/velocity must inherently increase. <br><br />
E) Because the torque being applied is constant, angular acceleration does not change (remember, acceleration is a measure of the rate of change of velocity!). <br><br />
<br />
===Middling===<br />
<br />
[[File:ProblemAndSolution.jpg]]<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
:::I had taken physics in high school, and a majority of the concepts covered in this class were familiar to me. However, I had never seen any of the material we covered in the last unit (like angular momentum, conservation of angular momentum, torque, etc.). This material was new and something I found interesting since it went a step further with the information we learned throughout the semester.<br />
[[File:HaloGameplay.jpg|420px|thumb|right|Example of physics being used to model the motion of vehicles in Halo 2]]<br />
#How is it connected to your major? Is there an interesting industrial application?<br />
:::My major is Computer Science, so I cannot really draw a clear line between my current coursework and this topic. That being said, physics is, of course, used in computer science. A good example would be in programming games where most interactions between objects involve physics of some kind, and the programmers/game designers want to model realistic situations in game. <br><br />
:::Another example that never really dawned upon me until about halfway through the semester was that both topics require a decent level skill in problem solving/reasoning. I've liked physics this semester because (and I guess this just applies to math in general) it's almost beautiful just to see how, in the end, everything works out and makes sense. Throughout the semester, I've never had a moment during class where I've flat out said, "No, that doesn't make sense" simply because that's never happened. I've never been a huge fan of physics, but even I can appreciate something that comes together so well.<br />
<br />
==History==<br />
<br />
This concept doesn't have it's own history since it's just a section under torque, so refer to http://www.physicsbook.gatech.edu/Torque#History for more information.<br />
<br />
== See also ==<br />
<br />
A general description of torque:<br />
http://www.physicsbook.gatech.edu/Torque<br />
<br />
===External links===<br />
[https://www.youtube.com/watch?v=mvzSjRFQbHE A brief overview on systems with non-zero torque]<br />
<br />
==References==<br />
<br />
Matters and Interactions: 4th Edition <br><br />
WebAssign <br><br />
College Physics: Ninth Edition by Raymond Serway and Chris Vuille <br><br />
[[Category:Angular Momentum]]</div>Nvohra3http://www.physicsbook.gatech.edu/index.php?title=Systems_with_Nonzero_Torque&diff=20371Systems with Nonzero Torque2015-12-08T04:11:10Z<p>Nvohra3: /* Connectedness */</p>
<hr />
<div>In certain systems, external torques have an effect on a system's angular momentum. Since these external forces do not sum to zero, we end up with a system with non-zero net torque.<br />
<br />
==The Main Idea==<br />
<br />
With previous systems involving torque, we've been fortunate enough to have systems where the net torque is non-zero, hence <math> \vec{L}_{final} = \vec{L}_{initial}. </math> <br><br />
See systems with zero net torque in "See Also" section below for more information. <br><br />
<br />
However, we're not always fortunate enough to have such systems. In such cases, our computations become a little more complicated, and we'll see how below.<br />
<br />
===A Mathematical Model===<br />
<br />
The angular momentum principle is the following: <math>{\frac{d\vec{L}}{dt}}= \vec{r} * \vec{F}_{net} = \vec{т}_{net} </math> <br><br />
As previously mentioned, we'll now look at the case where <math> \vec{F}_{net} </math> is NOT equal to 0.<br />
<br />
===How to Model in VPython===<br />
The following code should be self explanatory and can be used as a template for modeling a system involving torque.<br />
Important things to note are the use of cross() to calculate the cross product between two vectors and sphere.rotate() to rotate a sphere object around some axis at some angle.<br />
# -*- coding: utf-8 -*-<br />
from __future__ import division<br />
from visual import *<br />
<br />
NUM_LOOP_ITERATIONS = 5000 # Arbitrarily chose 5000<br />
wheel = sphere(pos = vector(0, 0, 0), radius = 10, color = color.cyan, mass = 5)<br />
axisOfRotation = vector(5, 0, 0) # Axis of rotation of system<br />
force = vector(5, 0, 0) # Force acting on system<br />
delta_t = 1<br />
t = 0<br />
angularMomentum= vector(20, 0, 0) # Initial angular momentum<br />
omega = 40 # Initial angular speed<br />
inertia = (wheel.mass * wheel.radius ** 2)/12 # Calculating intertia; ML^2 / 12<br />
dtheta = 0<br />
while t < 5000:<br />
rate(500)<br />
torque = cross(wheel.pos, force) # torque = position x force<br />
angularMomentum += torque * delta_t # Update angular momentum<br />
omega = angularMomentum / inertia<br />
omegaScalar = dot(omega, norm(axisOfRotation))<br />
dtheta += omegaScalar * delta_t<br />
wheel.rotate(angle=dtheta, axis = axisOfRotation, origin = wheel.pos)<br />
t += delta_t<br />
<br />
==Examples==<br />
===Simple===<br />
If a constant net torque (non-zero) is exerted on an object, which of the following quantities cannot be constant? <br><br />
A) Moment of inertia <br><br />
B) Center of mass <br><br />
C) Angular momentum <br><br />
D) Angular velocity <br><br />
E) Angular acceleration <br><br />
<br><br />
Solution/Explanation: <br><br />
C, D. Why? <br><br />
A) Moment of inertia does not change depending on whether torque is exerted on an object; moment of inertia depends on the object and axis of rotation, nothing more. <br><br />
B) Center of mass doesn't change with applied torque as well. <br><br />
C) Angular momentum is equal to inertia times angular speed, and we establish below that angular velocity changes. <br><br />
D) Angular velocity changes since a constant force is being applied to the object, so it's speed/velocity must inherently increase. <br><br />
E) Because the torque being applied is constant, angular acceleration does not change (remember, acceleration is a measure of the rate of change of velocity!). <br><br />
<br />
===Middling===<br />
<br />
[[File:ProblemAndSolution.jpg]]<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
:::I had taken physics in high school, and a majority of the concepts covered in this class were familiar to me. However, I had never seen any of the material we covered in the last unit (like angular momentum, conservation of angular momentum, torque, etc.). This material was new and something I found interesting since it went a step further with the information we learned throughout the semester.<br />
#How is it connected to your major? Is there an interesting industrial application?<br />
[[File:HaloGameplay.jpg|400px|thumb|right|Example of physics being used to model the motion of vehicles in Halo 2]]<br />
:::My major is Computer Science, so I cannot really draw a clear line between my current coursework and this topic. That being said, physics is, of course, used in computer science. A good example would be in programming games where most interactions between objects involve physics of some kind, and the programmers/game designers want to model realistic situations in game. <br><br />
:::Another example that never really dawned upon me until about halfway through the semester was that both topics require a decent level skill in problem solving/reasoning. I've liked physics this semester because (and I guess this just applies to math in general) it's almost beautiful just to see how, in the end, everything works out and makes sense. Throughout the semester, I've never had a moment during class where I've flat out said, "No, that doesn't make sense" simply because that's never happened. I've never been a huge fan of physics, but even I can appreciate something that comes together so well.<br />
<br />
==History==<br />
<br />
This concept doesn't have it's own history since it's just a section under torque, so refer to http://www.physicsbook.gatech.edu/Torque#History for more information.<br />
<br />
== See also ==<br />
<br />
A general description of torque:<br />
http://www.physicsbook.gatech.edu/Torque<br />
<br />
===External links===<br />
[https://www.youtube.com/watch?v=mvzSjRFQbHE A brief overview on systems with non-zero torque]<br />
<br />
==References==<br />
<br />
Matters and Interactions: 4th Edition <br><br />
WebAssign <br><br />
College Physics: Ninth Edition by Raymond Serway and Chris Vuille <br><br />
[[Category:Angular Momentum]]</div>Nvohra3http://www.physicsbook.gatech.edu/index.php?title=Systems_with_Nonzero_Torque&diff=20370Systems with Nonzero Torque2015-12-08T04:06:14Z<p>Nvohra3: /* Connectedness */</p>
<hr />
<div>In certain systems, external torques have an effect on a system's angular momentum. Since these external forces do not sum to zero, we end up with a system with non-zero net torque.<br />
<br />
==The Main Idea==<br />
<br />
With previous systems involving torque, we've been fortunate enough to have systems where the net torque is non-zero, hence <math> \vec{L}_{final} = \vec{L}_{initial}. </math> <br><br />
See systems with zero net torque in "See Also" section below for more information. <br><br />
<br />
However, we're not always fortunate enough to have such systems. In such cases, our computations become a little more complicated, and we'll see how below.<br />
<br />
===A Mathematical Model===<br />
<br />
The angular momentum principle is the following: <math>{\frac{d\vec{L}}{dt}}= \vec{r} * \vec{F}_{net} = \vec{т}_{net} </math> <br><br />
As previously mentioned, we'll now look at the case where <math> \vec{F}_{net} </math> is NOT equal to 0.<br />
<br />
===How to Model in VPython===<br />
The following code should be self explanatory and can be used as a template for modeling a system involving torque.<br />
Important things to note are the use of cross() to calculate the cross product between two vectors and sphere.rotate() to rotate a sphere object around some axis at some angle.<br />
# -*- coding: utf-8 -*-<br />
from __future__ import division<br />
from visual import *<br />
<br />
NUM_LOOP_ITERATIONS = 5000 # Arbitrarily chose 5000<br />
wheel = sphere(pos = vector(0, 0, 0), radius = 10, color = color.cyan, mass = 5)<br />
axisOfRotation = vector(5, 0, 0) # Axis of rotation of system<br />
force = vector(5, 0, 0) # Force acting on system<br />
delta_t = 1<br />
t = 0<br />
angularMomentum= vector(20, 0, 0) # Initial angular momentum<br />
omega = 40 # Initial angular speed<br />
inertia = (wheel.mass * wheel.radius ** 2)/12 # Calculating intertia; ML^2 / 12<br />
dtheta = 0<br />
while t < 5000:<br />
rate(500)<br />
torque = cross(wheel.pos, force) # torque = position x force<br />
angularMomentum += torque * delta_t # Update angular momentum<br />
omega = angularMomentum / inertia<br />
omegaScalar = dot(omega, norm(axisOfRotation))<br />
dtheta += omegaScalar * delta_t<br />
wheel.rotate(angle=dtheta, axis = axisOfRotation, origin = wheel.pos)<br />
t += delta_t<br />
<br />
==Examples==<br />
===Simple===<br />
If a constant net torque (non-zero) is exerted on an object, which of the following quantities cannot be constant? <br><br />
A) Moment of inertia <br><br />
B) Center of mass <br><br />
C) Angular momentum <br><br />
D) Angular velocity <br><br />
E) Angular acceleration <br><br />
<br><br />
Solution/Explanation: <br><br />
C, D. Why? <br><br />
A) Moment of inertia does not change depending on whether torque is exerted on an object; moment of inertia depends on the object and axis of rotation, nothing more. <br><br />
B) Center of mass doesn't change with applied torque as well. <br><br />
C) Angular momentum is equal to inertia times angular speed, and we establish below that angular velocity changes. <br><br />
D) Angular velocity changes since a constant force is being applied to the object, so it's speed/velocity must inherently increase. <br><br />
E) Because the torque being applied is constant, angular acceleration does not change (remember, acceleration is a measure of the rate of change of velocity!). <br><br />
<br />
===Middling===<br />
<br />
[[File:ProblemAndSolution.jpg]]<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
:::I had taken physics in high school, and a majority of the concepts covered in this class were familiar to me. However, I had never seen any of the material we covered in the last unit (like angular momentum, conservation of angular momentum, torque, etc.). This material was new and something I found interesting since it went a step further with the information we learned throughout the semester.<br />
#How is it connected to your major? Is there an interesting industrial application?<br />
:::My major is Computer Science, so I cannot really draw a clear line between my current coursework and this topic. That being said, physics is, of course, used in computer science. A good example would be in programming games where most interactions between objects involve physics of some kind, and the programmers/game designers want to model realistic situations in game. <br><br />
[[File:HaloGameplay.jpg|200px|thumb|left|Example of how physics is used in common games]]<br />
<br />
Another example that never really dawned upon me until about halfway through the semester was that both topics require a decent level skill in problem solving/reasoning. I've liked physics this semester because (and I guess this just applies to math in general) it's almost beautiful just to see how, in the end, everything works out and makes sense. Throughout the semester, I've never had a moment during class where I've flat out said, "No, that doesn't make sense" simply because that's never happened. I've never been a huge fan of physics, but even I can appreciate something that comes together so well.<br />
<br />
==History==<br />
<br />
This concept doesn't have it's own history since it's just a section under torque, so refer to http://www.physicsbook.gatech.edu/Torque#History for more information.<br />
<br />
== See also ==<br />
<br />
A general description of torque:<br />
http://www.physicsbook.gatech.edu/Torque<br />
<br />
===External links===<br />
[https://www.youtube.com/watch?v=mvzSjRFQbHE A brief overview on systems with non-zero torque]<br />
<br />
==References==<br />
<br />
Matters and Interactions: 4th Edition <br><br />
WebAssign <br><br />
College Physics: Ninth Edition by Raymond Serway and Chris Vuille <br><br />
[[Category:Angular Momentum]]</div>Nvohra3http://www.physicsbook.gatech.edu/index.php?title=File:HaloGameplay.jpg&diff=20369File:HaloGameplay.jpg2015-12-08T04:05:13Z<p>Nvohra3: </p>
<hr />
<div></div>Nvohra3http://www.physicsbook.gatech.edu/index.php?title=Systems_with_Nonzero_Torque&diff=20367Systems with Nonzero Torque2015-12-08T03:45:55Z<p>Nvohra3: /* How to Model in VPython */</p>
<hr />
<div>In certain systems, external torques have an effect on a system's angular momentum. Since these external forces do not sum to zero, we end up with a system with non-zero net torque.<br />
<br />
==The Main Idea==<br />
<br />
With previous systems involving torque, we've been fortunate enough to have systems where the net torque is non-zero, hence <math> \vec{L}_{final} = \vec{L}_{initial}. </math> <br><br />
See systems with zero net torque in "See Also" section below for more information. <br><br />
<br />
However, we're not always fortunate enough to have such systems. In such cases, our computations become a little more complicated, and we'll see how below.<br />
<br />
===A Mathematical Model===<br />
<br />
The angular momentum principle is the following: <math>{\frac{d\vec{L}}{dt}}= \vec{r} * \vec{F}_{net} = \vec{т}_{net} </math> <br><br />
As previously mentioned, we'll now look at the case where <math> \vec{F}_{net} </math> is NOT equal to 0.<br />
<br />
===How to Model in VPython===<br />
The following code should be self explanatory and can be used as a template for modeling a system involving torque.<br />
Important things to note are the use of cross() to calculate the cross product between two vectors and sphere.rotate() to rotate a sphere object around some axis at some angle.<br />
# -*- coding: utf-8 -*-<br />
from __future__ import division<br />
from visual import *<br />
<br />
NUM_LOOP_ITERATIONS = 5000 # Arbitrarily chose 5000<br />
wheel = sphere(pos = vector(0, 0, 0), radius = 10, color = color.cyan, mass = 5)<br />
axisOfRotation = vector(5, 0, 0) # Axis of rotation of system<br />
force = vector(5, 0, 0) # Force acting on system<br />
delta_t = 1<br />
t = 0<br />
angularMomentum= vector(20, 0, 0) # Initial angular momentum<br />
omega = 40 # Initial angular speed<br />
inertia = (wheel.mass * wheel.radius ** 2)/12 # Calculating intertia; ML^2 / 12<br />
dtheta = 0<br />
while t < 5000:<br />
rate(500)<br />
torque = cross(wheel.pos, force) # torque = position x force<br />
angularMomentum += torque * delta_t # Update angular momentum<br />
omega = angularMomentum / inertia<br />
omegaScalar = dot(omega, norm(axisOfRotation))<br />
dtheta += omegaScalar * delta_t<br />
wheel.rotate(angle=dtheta, axis = axisOfRotation, origin = wheel.pos)<br />
t += delta_t<br />
<br />
==Examples==<br />
===Simple===<br />
If a constant net torque (non-zero) is exerted on an object, which of the following quantities cannot be constant? <br><br />
A) Moment of inertia <br><br />
B) Center of mass <br><br />
C) Angular momentum <br><br />
D) Angular velocity <br><br />
E) Angular acceleration <br><br />
<br><br />
Solution/Explanation: <br><br />
C, D. Why? <br><br />
A) Moment of inertia does not change depending on whether torque is exerted on an object; moment of inertia depends on the object and axis of rotation, nothing more. <br><br />
B) Center of mass doesn't change with applied torque as well. <br><br />
C) Angular momentum is equal to inertia times angular speed, and we establish below that angular velocity changes. <br><br />
D) Angular velocity changes since a constant force is being applied to the object, so it's speed/velocity must inherently increase. <br><br />
E) Because the torque being applied is constant, angular acceleration does not change (remember, acceleration is a measure of the rate of change of velocity!). <br><br />
<br />
===Middling===<br />
<br />
[[File:ProblemAndSolution.jpg]]<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
:::I had taken physics in high school, and a majority of the concepts covered in this class were familiar to me. However, I had never seen any of the material we covered in the last unit (like angular momentum, conservation of angular momentum, torque, etc.). This material was new and something I found interesting since it went a step further with the information we learned throughout the semester.<br />
#How is it connected to your major? Is there an interesting industrial application?<br />
:::My major is Computer Science, so I cannot really draw a clear line between my current coursework and this topic. That being said, physics is, of course, used in computer science. A good example would be in programming games where most interactions between objects involve physics of some kind, and the programmers/game designers want to model realistic situations in game. Another example that never really dawned upon me until about halfway through the semester was that both topics require a decent level skill in problem solving/reasoning. I've liked physics this semester because (and I guess this just applies to math in general) it's almost beautiful just to see how, in the end, everything works out and makes sense. Throughout the semester, I've never had a moment during class where I've flat out said, "No, that doesn't make sense" simply because that's never happened. I've never been a huge fan of physics, but even I can appreciate something that comes together so well.<br />
<br />
==History==<br />
<br />
This concept doesn't have it's own history since it's just a section under torque, so refer to http://www.physicsbook.gatech.edu/Torque#History for more information.<br />
<br />
== See also ==<br />
<br />
A general description of torque:<br />
http://www.physicsbook.gatech.edu/Torque<br />
<br />
===External links===<br />
[https://www.youtube.com/watch?v=mvzSjRFQbHE A brief overview on systems with non-zero torque]<br />
<br />
==References==<br />
<br />
Matters and Interactions: 4th Edition <br><br />
WebAssign <br><br />
College Physics: Ninth Edition by Raymond Serway and Chris Vuille <br><br />
[[Category:Angular Momentum]]</div>Nvohra3http://www.physicsbook.gatech.edu/index.php?title=Systems_with_Nonzero_Torque&diff=20365Systems with Nonzero Torque2015-12-08T03:44:18Z<p>Nvohra3: /* How to Model in VPython */</p>
<hr />
<div>In certain systems, external torques have an effect on a system's angular momentum. Since these external forces do not sum to zero, we end up with a system with non-zero net torque.<br />
<br />
==The Main Idea==<br />
<br />
With previous systems involving torque, we've been fortunate enough to have systems where the net torque is non-zero, hence <math> \vec{L}_{final} = \vec{L}_{initial}. </math> <br><br />
See systems with zero net torque in "See Also" section below for more information. <br><br />
<br />
However, we're not always fortunate enough to have such systems. In such cases, our computations become a little more complicated, and we'll see how below.<br />
<br />
===A Mathematical Model===<br />
<br />
The angular momentum principle is the following: <math>{\frac{d\vec{L}}{dt}}= \vec{r} * \vec{F}_{net} = \vec{т}_{net} </math> <br><br />
As previously mentioned, we'll now look at the case where <math> \vec{F}_{net} </math> is NOT equal to 0.<br />
<br />
===How to Model in VPython===<br />
The following code should be self explanatory and can be used as a template for modeling a system involving torque:<br />
# -*- coding: utf-8 -*-<br />
from __future__ import division<br />
from visual import *<br />
<br />
NUM_LOOP_ITERATIONS = 5000 # Arbitrarily chose 5000<br />
wheel = sphere(pos = vector(0, 0, 0), radius = 10, color = color.cyan, mass = 5)<br />
axisOfRotation = vector(5, 0, 0) # Axis of rotation of system<br />
force = vector(5, 0, 0) # Force acting on system<br />
delta_t = 1<br />
t = 0<br />
angularMomentum= vector(20, 0, 0) # Initial angular momentum<br />
omega = 40 # Initial angular speed<br />
inertia = (wheel.mass * wheel.radius ** 2)/12 # Calculating intertia; ML^2 / 12<br />
dtheta = 0<br />
while t < 5000:<br />
rate(500)<br />
torque = cross(wheel.pos, force) # torque = position x force<br />
angularMomentum += torque * delta_t<br />
omega = angularMomentum / inertia<br />
omegaScalar = dot(omega, norm(axisOfRotation))<br />
dtheta += omegaScalar * delta_t<br />
wheel.rotate(angle=dtheta, axis = axisOfRotation, origin = wheel.pos)<br />
t += delta_t<br />
<br />
==Examples==<br />
===Simple===<br />
If a constant net torque (non-zero) is exerted on an object, which of the following quantities cannot be constant? <br><br />
A) Moment of inertia <br><br />
B) Center of mass <br><br />
C) Angular momentum <br><br />
D) Angular velocity <br><br />
E) Angular acceleration <br><br />
<br><br />
Solution/Explanation: <br><br />
C, D. Why? <br><br />
A) Moment of inertia does not change depending on whether torque is exerted on an object; moment of inertia depends on the object and axis of rotation, nothing more. <br><br />
B) Center of mass doesn't change with applied torque as well. <br><br />
C) Angular momentum is equal to inertia times angular speed, and we establish below that angular velocity changes. <br><br />
D) Angular velocity changes since a constant force is being applied to the object, so it's speed/velocity must inherently increase. <br><br />
E) Because the torque being applied is constant, angular acceleration does not change (remember, acceleration is a measure of the rate of change of velocity!). <br><br />
<br />
===Middling===<br />
<br />
[[File:ProblemAndSolution.jpg]]<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
:::I had taken physics in high school, and a majority of the concepts covered in this class were familiar to me. However, I had never seen any of the material we covered in the last unit (like angular momentum, conservation of angular momentum, torque, etc.). This material was new and something I found interesting since it went a step further with the information we learned throughout the semester.<br />
#How is it connected to your major? Is there an interesting industrial application?<br />
:::My major is Computer Science, so I cannot really draw a clear line between my current coursework and this topic. That being said, physics is, of course, used in computer science. A good example would be in programming games where most interactions between objects involve physics of some kind, and the programmers/game designers want to model realistic situations in game. Another example that never really dawned upon me until about halfway through the semester was that both topics require a decent level skill in problem solving/reasoning. I've liked physics this semester because (and I guess this just applies to math in general) it's almost beautiful just to see how, in the end, everything works out and makes sense. Throughout the semester, I've never had a moment during class where I've flat out said, "No, that doesn't make sense" simply because that's never happened. I've never been a huge fan of physics, but even I can appreciate something that comes together so well.<br />
<br />
==History==<br />
<br />
This concept doesn't have it's own history since it's just a section under torque, so refer to http://www.physicsbook.gatech.edu/Torque#History for more information.<br />
<br />
== See also ==<br />
<br />
A general description of torque:<br />
http://www.physicsbook.gatech.edu/Torque<br />
<br />
===External links===<br />
[https://www.youtube.com/watch?v=mvzSjRFQbHE A brief overview on systems with non-zero torque]<br />
<br />
==References==<br />
<br />
Matters and Interactions: 4th Edition <br><br />
WebAssign <br><br />
College Physics: Ninth Edition by Raymond Serway and Chris Vuille <br><br />
[[Category:Angular Momentum]]</div>Nvohra3http://www.physicsbook.gatech.edu/index.php?title=Systems_with_Nonzero_Torque&diff=20364Systems with Nonzero Torque2015-12-08T03:43:36Z<p>Nvohra3: /* The Main Idea */</p>
<hr />
<div>In certain systems, external torques have an effect on a system's angular momentum. Since these external forces do not sum to zero, we end up with a system with non-zero net torque.<br />
<br />
==The Main Idea==<br />
<br />
With previous systems involving torque, we've been fortunate enough to have systems where the net torque is non-zero, hence <math> \vec{L}_{final} = \vec{L}_{initial}. </math> <br><br />
See systems with zero net torque in "See Also" section below for more information. <br><br />
<br />
However, we're not always fortunate enough to have such systems. In such cases, our computations become a little more complicated, and we'll see how below.<br />
<br />
===A Mathematical Model===<br />
<br />
The angular momentum principle is the following: <math>{\frac{d\vec{L}}{dt}}= \vec{r} * \vec{F}_{net} = \vec{т}_{net} </math> <br><br />
As previously mentioned, we'll now look at the case where <math> \vec{F}_{net} </math> is NOT equal to 0.<br />
<br />
===How to Model in VPython===<br />
The following code should be self explanatory and can be used as a template for modeling a system involving torque:<br />
# -*- coding: utf-8 -*-<br />
from __future__ import division<br />
from visual import *<br />
<br />
NUM_LOOP_ITERATIONS = 5000 # Arbitrarily chose 5000<br />
wheel = sphere(pos = vector(0, 0, 0), radius = 10, color = color.cyan, mass = 5)<br />
axisOfRotation = vector(5, 0, 0) # Axis of rotation of system<br />
force = vector(5, 0, 0) # Force acting on system<br />
delta_t = 1<br />
t = 0<br />
angularMomentum= vector(20, 0, 0) # Initial angular momentum<br />
omega = 40 # Initial angular speed<br />
inertia = (wheel.mass * wheel.radius ** 2)/12 # Calculating intertia; ML^2 / 12<br />
dtheta = 0<br />
while t < 5000:<br />
rate(500)<br />
torque = cross(wheel.pos, force) # torque = position x force<br />
angularMomentum += torque * delta_t<br />
omega = angularMomentum / inertia<br />
omegaScalar = dot(omega, norm(axisOfRotation))<br />
dtheta += omegaScalar * delta_t<br />
wheel.rotate(angle=dtheta, axis = axisOfRotation, origin = wheel.pos)<br />
t += delta_t<br />
<br />
==Examples==<br />
===Simple===<br />
If a constant net torque (non-zero) is exerted on an object, which of the following quantities cannot be constant? <br><br />
A) Moment of inertia <br><br />
B) Center of mass <br><br />
C) Angular momentum <br><br />
D) Angular velocity <br><br />
E) Angular acceleration <br><br />
<br><br />
Solution/Explanation: <br><br />
C, D. Why? <br><br />
A) Moment of inertia does not change depending on whether torque is exerted on an object; moment of inertia depends on the object and axis of rotation, nothing more. <br><br />
B) Center of mass doesn't change with applied torque as well. <br><br />
C) Angular momentum is equal to inertia times angular speed, and we establish below that angular velocity changes. <br><br />
D) Angular velocity changes since a constant force is being applied to the object, so it's speed/velocity must inherently increase. <br><br />
E) Because the torque being applied is constant, angular acceleration does not change (remember, acceleration is a measure of the rate of change of velocity!). <br><br />
<br />
===Middling===<br />
<br />
[[File:ProblemAndSolution.jpg]]<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
:::I had taken physics in high school, and a majority of the concepts covered in this class were familiar to me. However, I had never seen any of the material we covered in the last unit (like angular momentum, conservation of angular momentum, torque, etc.). This material was new and something I found interesting since it went a step further with the information we learned throughout the semester.<br />
#How is it connected to your major? Is there an interesting industrial application?<br />
:::My major is Computer Science, so I cannot really draw a clear line between my current coursework and this topic. That being said, physics is, of course, used in computer science. A good example would be in programming games where most interactions between objects involve physics of some kind, and the programmers/game designers want to model realistic situations in game. Another example that never really dawned upon me until about halfway through the semester was that both topics require a decent level skill in problem solving/reasoning. I've liked physics this semester because (and I guess this just applies to math in general) it's almost beautiful just to see how, in the end, everything works out and makes sense. Throughout the semester, I've never had a moment during class where I've flat out said, "No, that doesn't make sense" simply because that's never happened. I've never been a huge fan of physics, but even I can appreciate something that comes together so well.<br />
<br />
==History==<br />
<br />
This concept doesn't have it's own history since it's just a section under torque, so refer to http://www.physicsbook.gatech.edu/Torque#History for more information.<br />
<br />
== See also ==<br />
<br />
A general description of torque:<br />
http://www.physicsbook.gatech.edu/Torque<br />
<br />
===External links===<br />
[https://www.youtube.com/watch?v=mvzSjRFQbHE A brief overview on systems with non-zero torque]<br />
<br />
==References==<br />
<br />
Matters and Interactions: 4th Edition <br><br />
WebAssign <br><br />
College Physics: Ninth Edition by Raymond Serway and Chris Vuille <br><br />
[[Category:Angular Momentum]]</div>Nvohra3http://www.physicsbook.gatech.edu/index.php?title=Systems_with_Nonzero_Torque&diff=20327Systems with Nonzero Torque2015-12-07T16:49:59Z<p>Nvohra3: /* Simple */</p>
<hr />
<div>In certain systems, external torques have an effect on a system's angular momentum. Since these external forces do not sum to zero, we end up with a system with non-zero net torque.<br />
<br />
==The Main Idea==<br />
<br />
With previous systems involving torque, we've been fortunate enough to have systems where the net torque is non-zero, hence <math> \vec{L}_{final} = \vec{L}_{initial}. </math> <br><br />
See systems with zero net torque in "See Also" section below for more information. <br><br />
<br />
However, we're not always fortunate enough to have such systems. In such cases, our computations become a little more complicated, and we'll see how below.<br />
<br />
===A Mathematical Model===<br />
<br />
The angular momentum principle is the following: <math>{\frac{d\vec{L}}{dt}}= \vec{r} * \vec{F}_{net} = \vec{т}_{net} </math> <br><br />
As previously mentioned, we'll now look at the case where <math> \vec{F}_{net} </math> is NOT equal to 0.<br />
<br />
==Examples==<br />
===Simple===<br />
If a constant net torque (non-zero) is exerted on an object, which of the following quantities cannot be constant? <br><br />
A) Moment of inertia <br><br />
B) Center of mass <br><br />
C) Angular momentum <br><br />
D) Angular velocity <br><br />
E) Angular acceleration <br><br />
<br><br />
Solution/Explanation: <br><br />
C, D. Why? <br><br />
A) Moment of inertia does not change depending on whether torque is exerted on an object; moment of inertia depends on the object and axis of rotation, nothing more. <br><br />
B) Center of mass doesn't change with applied torque as well. <br><br />
C) Angular momentum is equal to inertia times angular speed, and we establish below that angular velocity changes. <br><br />
D) Angular velocity changes since a constant force is being applied to the object, so it's speed/velocity must inherently increase. <br><br />
E) Because the torque being applied is constant, angular acceleration does not change (remember, acceleration is a measure of the rate of change of velocity!). <br><br />
<br />
===Middling===<br />
<br />
[[File:ProblemAndSolution.jpg]]<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
:::I had taken physics in high school, and a majority of the concepts covered in this class were familiar to me. However, I had never seen any of the material we covered in the last unit (like angular momentum, conservation of angular momentum, torque, etc.). This material was new and something I found interesting since it went a step further with the information we learned throughout the semester.<br />
#How is it connected to your major? Is there an interesting industrial application?<br />
:::My major is Computer Science, so I cannot really draw a clear line between my current coursework and this topic. That being said, physics is, of course, used in computer science. A good example would be in programming games where most interactions between objects involve physics of some kind, and the programmers/game designers want to model realistic situations in game. Another example that never really dawned upon me until about halfway through the semester was that both topics require a decent level skill in problem solving/reasoning. I've liked physics this semester because (and I guess this just applies to math in general) it's almost beautiful just to see how, in the end, everything works out and makes sense. Throughout the semester, I've never had a moment during class where I've flat out said, "No, that doesn't make sense" simply because that's never happened. I've never been a huge fan of physics, but even I can appreciate something that comes together so well.<br />
<br />
==History==<br />
<br />
This concept doesn't have it's own history since it's just a section under torque, so refer to http://www.physicsbook.gatech.edu/Torque#History for more information.<br />
<br />
== See also ==<br />
<br />
A general description of torque:<br />
http://www.physicsbook.gatech.edu/Torque<br />
<br />
===External links===<br />
[https://www.youtube.com/watch?v=mvzSjRFQbHE A brief overview on systems with non-zero torque]<br />
<br />
==References==<br />
<br />
Matters and Interactions: 4th Edition <br><br />
WebAssign <br><br />
College Physics: Ninth Edition by Raymond Serway and Chris Vuille <br><br />
[[Category:Angular Momentum]]</div>Nvohra3http://www.physicsbook.gatech.edu/index.php?title=Systems_with_Nonzero_Torque&diff=20326Systems with Nonzero Torque2015-12-07T16:45:39Z<p>Nvohra3: /* Middling */</p>
<hr />
<div>In certain systems, external torques have an effect on a system's angular momentum. Since these external forces do not sum to zero, we end up with a system with non-zero net torque.<br />
<br />
==The Main Idea==<br />
<br />
With previous systems involving torque, we've been fortunate enough to have systems where the net torque is non-zero, hence <math> \vec{L}_{final} = \vec{L}_{initial}. </math> <br><br />
See systems with zero net torque in "See Also" section below for more information. <br><br />
<br />
However, we're not always fortunate enough to have such systems. In such cases, our computations become a little more complicated, and we'll see how below.<br />
<br />
===A Mathematical Model===<br />
<br />
The angular momentum principle is the following: <math>{\frac{d\vec{L}}{dt}}= \vec{r} * \vec{F}_{net} = \vec{т}_{net} </math> <br><br />
As previously mentioned, we'll now look at the case where <math> \vec{F}_{net} </math> is NOT equal to 0.<br />
<br />
==Examples==<br />
===Simple===<br />
* Example taken from College Physics textbook<br />
A constant net nonzero torque is exerted on an object. Which of the following quantities cannot be constant for this object? <br><br />
A) Moment of inertia <br><br />
B) Center of mass <br><br />
C) Angular momentum <br><br />
D) Angular velocity <br><br />
E) Angular acceleration <br><br />
<br><br />
Solution/Explanation: <br><br />
C, D. Why? <br><br />
A) Moment of inertia does not change depending on whether torque is exerted on an object; moment of inertia depends on the object and axis of rotation, nothing more. <br><br />
B) Center of mass doesn't change with applied torque as well. <br><br />
C) Angular momentum is equal to inertia times angular speed, and we establish below that angular velocity changes. <br><br />
D) Angular velocity changes since a constant force is being applied to the object, so it's speed/velocity must inherently increase. <br><br />
E) Because the torque being applied is constant, angular acceleration does not change (remember, acceleration is a measure of the rate of change of velocity!). <br><br />
<br />
===Middling===<br />
<br />
[[File:ProblemAndSolution.jpg]]<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
:::I had taken physics in high school, and a majority of the concepts covered in this class were familiar to me. However, I had never seen any of the material we covered in the last unit (like angular momentum, conservation of angular momentum, torque, etc.). This material was new and something I found interesting since it went a step further with the information we learned throughout the semester.<br />
#How is it connected to your major? Is there an interesting industrial application?<br />
:::My major is Computer Science, so I cannot really draw a clear line between my current coursework and this topic. That being said, physics is, of course, used in computer science. A good example would be in programming games where most interactions between objects involve physics of some kind, and the programmers/game designers want to model realistic situations in game. Another example that never really dawned upon me until about halfway through the semester was that both topics require a decent level skill in problem solving/reasoning. I've liked physics this semester because (and I guess this just applies to math in general) it's almost beautiful just to see how, in the end, everything works out and makes sense. Throughout the semester, I've never had a moment during class where I've flat out said, "No, that doesn't make sense" simply because that's never happened. I've never been a huge fan of physics, but even I can appreciate something that comes together so well.<br />
<br />
==History==<br />
<br />
This concept doesn't have it's own history since it's just a section under torque, so refer to http://www.physicsbook.gatech.edu/Torque#History for more information.<br />
<br />
== See also ==<br />
<br />
A general description of torque:<br />
http://www.physicsbook.gatech.edu/Torque<br />
<br />
===External links===<br />
[https://www.youtube.com/watch?v=mvzSjRFQbHE A brief overview on systems with non-zero torque]<br />
<br />
==References==<br />
<br />
Matters and Interactions: 4th Edition <br><br />
WebAssign <br><br />
College Physics: Ninth Edition by Raymond Serway and Chris Vuille <br><br />
[[Category:Angular Momentum]]</div>Nvohra3http://www.physicsbook.gatech.edu/index.php?title=File:ProblemAndSolution.jpg&diff=20325File:ProblemAndSolution.jpg2015-12-07T16:39:51Z<p>Nvohra3: </p>
<hr />
<div></div>Nvohra3http://www.physicsbook.gatech.edu/index.php?title=Systems_with_Nonzero_Torque&diff=19929Systems with Nonzero Torque2015-12-06T04:59:00Z<p>Nvohra3: /* A Computational Model */</p>
<hr />
<div>In certain systems, external torques have an effect on a system's angular momentum. Since these external forces do not sum to zero, we end up with a system with non-zero net torque.<br />
<br />
==The Main Idea==<br />
<br />
With previous systems involving torque, we've been fortunate enough to have systems where the net torque is non-zero, hence <math> \vec{L}_{final} = \vec{L}_{initial}. </math> <br><br />
See systems with zero net torque in "See Also" section below for more information. <br><br />
<br />
However, we're not always fortunate enough to have such systems. In such cases, our computations become a little more complicated, and we'll see how below.<br />
<br />
===A Mathematical Model===<br />
<br />
The angular momentum principle is the following: <math>{\frac{d\vec{L}}{dt}}= \vec{r} * \vec{F}_{net} = \vec{т}_{net} </math> <br><br />
As previously mentioned, we'll now look at the case where <math> \vec{F}_{net} </math> is NOT equal to 0.<br />
<br />
==Examples==<br />
===Simple===<br />
* Example taken from College Physics textbook<br />
A constant net nonzero torque is exerted on an object. Which of the following quantities cannot be constant for this object? <br><br />
A) Moment of inertia <br><br />
B) Center of mass <br><br />
C) Angular momentum <br><br />
D) Angular velocity <br><br />
E) Angular acceleration <br><br />
<br><br />
Solution/Explanation: <br><br />
C, D. Why? <br><br />
A) Moment of inertia does not change depending on whether torque is exerted on an object; moment of inertia depends on the object and axis of rotation, nothing more. <br><br />
B) Center of mass doesn't change with applied torque as well. <br><br />
C) Angular momentum is equal to inertia times angular speed, and we establish below that angular velocity changes. <br><br />
D) Angular velocity changes since a constant force is being applied to the object, so it's speed/velocity must inherently increase. <br><br />
E) Because the torque being applied is constant, angular acceleration does not change (remember, acceleration is a measure of the rate of change of velocity!). <br><br />
<br />
===Middling===<br />
* Example taken from Interactions and Matter: 4th Edition textbook<br />
[[File:Screen Shot 2015-12-05 at 9.47.39 PM.png]]<br />
<br />
[[File:Solution.jpg]]<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
:::I had taken physics in high school, and a majority of the concepts covered in this class were familiar to me. However, I had never seen any of the material we covered in the last unit (like angular momentum, conservation of angular momentum, torque, etc.). This material was new and something I found interesting since it went a step further with the information we learned throughout the semester.<br />
#How is it connected to your major? Is there an interesting industrial application?<br />
:::My major is Computer Science, so I cannot really draw a clear line between my current coursework and this topic. That being said, physics is, of course, used in computer science. A good example would be in programming games where most interactions between objects involve physics of some kind, and the programmers/game designers want to model realistic situations in game. Another example that never really dawned upon me until about halfway through the semester was that both topics require a decent level skill in problem solving/reasoning. I've liked physics this semester because (and I guess this just applies to math in general) it's almost beautiful just to see how, in the end, everything works out and makes sense. Throughout the semester, I've never had a moment during class where I've flat out said, "No, that doesn't make sense" simply because that's never happened. I've never been a huge fan of physics, but even I can appreciate something that comes together so well.<br />
<br />
==History==<br />
<br />
This concept doesn't have it's own history since it's just a section under torque, so refer to http://www.physicsbook.gatech.edu/Torque#History for more information.<br />
<br />
== See also ==<br />
<br />
A general description of torque:<br />
http://www.physicsbook.gatech.edu/Torque<br />
<br />
===External links===<br />
[https://www.youtube.com/watch?v=mvzSjRFQbHE A brief overview on systems with non-zero torque]<br />
<br />
==References==<br />
<br />
Matters and Interactions: 4th Edition <br><br />
WebAssign <br><br />
College Physics: Ninth Edition by Raymond Serway and Chris Vuille <br><br />
[[Category:Angular Momentum]]</div>Nvohra3http://www.physicsbook.gatech.edu/index.php?title=Systems_with_Nonzero_Torque&diff=19848Systems with Nonzero Torque2015-12-06T04:48:10Z<p>Nvohra3: /* Middling */</p>
<hr />
<div>In certain systems, external torques have an effect on a system's angular momentum. Since these external forces do not sum to zero, we end up with a system with non-zero net torque.<br />
<br />
==The Main Idea==<br />
<br />
With previous systems involving torque, we've been fortunate enough to have systems where the net torque is non-zero, hence <math> \vec{L}_{final} = \vec{L}_{initial}. </math> <br><br />
See systems with zero net torque in "See Also" section below for more information. <br><br />
<br />
However, we're not always fortunate enough to have such systems. In such cases, our computations become a little more complicated, and we'll see how below.<br />
<br />
===A Mathematical Model===<br />
<br />
The angular momentum principle is the following: <math>{\frac{d\vec{L}}{dt}}= \vec{r} * \vec{F}_{net} = \vec{т}_{net} </math> <br><br />
As previously mentioned, we'll now look at the case where <math> \vec{F}_{net} </math> is NOT equal to 0.<br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
===Simple===<br />
* Example taken from College Physics textbook<br />
A constant net nonzero torque is exerted on an object. Which of the following quantities cannot be constant for this object? <br><br />
A) Moment of inertia <br><br />
B) Center of mass <br><br />
C) Angular momentum <br><br />
D) Angular velocity <br><br />
E) Angular acceleration <br><br />
<br><br />
Solution/Explanation: <br><br />
C, D. Why? <br><br />
A) Moment of inertia does not change depending on whether torque is exerted on an object; moment of inertia depends on the object and axis of rotation, nothing more. <br><br />
B) Center of mass doesn't change with applied torque as well. <br><br />
C) Angular momentum is equal to inertia times angular speed, and we establish below that angular velocity changes. <br><br />
D) Angular velocity changes since a constant force is being applied to the object, so it's speed/velocity must inherently increase. <br><br />
E) Because the torque being applied is constant, angular acceleration does not change (remember, acceleration is a measure of the rate of change of velocity!). <br><br />
<br />
===Middling===<br />
* Example taken from Interactions and Matter: 4th Edition textbook<br />
[[File:Screen Shot 2015-12-05 at 9.47.39 PM.png]]<br />
<br />
[[File:Solution.jpg]]<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
:::I had taken physics in high school, and a majority of the concepts covered in this class were familiar to me. However, I had never seen any of the material we covered in the last unit (like angular momentum, conservation of angular momentum, torque, etc.). This material was new and something I found interesting since it went a step further with the information we learned throughout the semester.<br />
#How is it connected to your major? Is there an interesting industrial application?<br />
:::My major is Computer Science, so I cannot really draw a clear line between my current coursework and this topic. That being said, physics is, of course, used in computer science. A good example would be in programming games where most interactions between objects involve physics of some kind, and the programmers/game designers want to model realistic situations in game. Another example that never really dawned upon me until about halfway through the semester was that both topics require a decent level skill in problem solving/reasoning. I've liked physics this semester because (and I guess this just applies to math in general) it's almost beautiful just to see how, in the end, everything works out and makes sense. Throughout the semester, I've never had a moment during class where I've flat out said, "No, that doesn't make sense" simply because that's never happened. I've never been a huge fan of physics, but even I can appreciate something that comes together so well.<br />
<br />
==History==<br />
<br />
This concept doesn't have it's own history since it's just a section under torque, so refer to http://www.physicsbook.gatech.edu/Torque#History for more information.<br />
<br />
== See also ==<br />
<br />
A general description of torque:<br />
http://www.physicsbook.gatech.edu/Torque<br />
<br />
===External links===<br />
[https://www.youtube.com/watch?v=mvzSjRFQbHE A brief overview on systems with non-zero torque]<br />
<br />
==References==<br />
<br />
Matters and Interactions: 4th Edition <br><br />
WebAssign <br><br />
College Physics: Ninth Edition by Raymond Serway and Chris Vuille <br><br />
[[Category:Angular Momentum]]</div>Nvohra3http://www.physicsbook.gatech.edu/index.php?title=Systems_with_Nonzero_Torque&diff=19847Systems with Nonzero Torque2015-12-06T04:47:56Z<p>Nvohra3: /* Simple */</p>
<hr />
<div>In certain systems, external torques have an effect on a system's angular momentum. Since these external forces do not sum to zero, we end up with a system with non-zero net torque.<br />
<br />
==The Main Idea==<br />
<br />
With previous systems involving torque, we've been fortunate enough to have systems where the net torque is non-zero, hence <math> \vec{L}_{final} = \vec{L}_{initial}. </math> <br><br />
See systems with zero net torque in "See Also" section below for more information. <br><br />
<br />
However, we're not always fortunate enough to have such systems. In such cases, our computations become a little more complicated, and we'll see how below.<br />
<br />
===A Mathematical Model===<br />
<br />
The angular momentum principle is the following: <math>{\frac{d\vec{L}}{dt}}= \vec{r} * \vec{F}_{net} = \vec{т}_{net} </math> <br><br />
As previously mentioned, we'll now look at the case where <math> \vec{F}_{net} </math> is NOT equal to 0.<br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
===Simple===<br />
* Example taken from College Physics textbook<br />
A constant net nonzero torque is exerted on an object. Which of the following quantities cannot be constant for this object? <br><br />
A) Moment of inertia <br><br />
B) Center of mass <br><br />
C) Angular momentum <br><br />
D) Angular velocity <br><br />
E) Angular acceleration <br><br />
<br><br />
Solution/Explanation: <br><br />
C, D. Why? <br><br />
A) Moment of inertia does not change depending on whether torque is exerted on an object; moment of inertia depends on the object and axis of rotation, nothing more. <br><br />
B) Center of mass doesn't change with applied torque as well. <br><br />
C) Angular momentum is equal to inertia times angular speed, and we establish below that angular velocity changes. <br><br />
D) Angular velocity changes since a constant force is being applied to the object, so it's speed/velocity must inherently increase. <br><br />
E) Because the torque being applied is constant, angular acceleration does not change (remember, acceleration is a measure of the rate of change of velocity!). <br><br />
<br />
===Middling===<br />
[[File:Screen Shot 2015-12-05 at 9.47.39 PM.png]]<br />
<br />
[[File:Solution.jpg]]<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
:::I had taken physics in high school, and a majority of the concepts covered in this class were familiar to me. However, I had never seen any of the material we covered in the last unit (like angular momentum, conservation of angular momentum, torque, etc.). This material was new and something I found interesting since it went a step further with the information we learned throughout the semester.<br />
#How is it connected to your major? Is there an interesting industrial application?<br />
:::My major is Computer Science, so I cannot really draw a clear line between my current coursework and this topic. That being said, physics is, of course, used in computer science. A good example would be in programming games where most interactions between objects involve physics of some kind, and the programmers/game designers want to model realistic situations in game. Another example that never really dawned upon me until about halfway through the semester was that both topics require a decent level skill in problem solving/reasoning. I've liked physics this semester because (and I guess this just applies to math in general) it's almost beautiful just to see how, in the end, everything works out and makes sense. Throughout the semester, I've never had a moment during class where I've flat out said, "No, that doesn't make sense" simply because that's never happened. I've never been a huge fan of physics, but even I can appreciate something that comes together so well.<br />
<br />
==History==<br />
<br />
This concept doesn't have it's own history since it's just a section under torque, so refer to http://www.physicsbook.gatech.edu/Torque#History for more information.<br />
<br />
== See also ==<br />
<br />
A general description of torque:<br />
http://www.physicsbook.gatech.edu/Torque<br />
<br />
===External links===<br />
[https://www.youtube.com/watch?v=mvzSjRFQbHE A brief overview on systems with non-zero torque]<br />
<br />
==References==<br />
<br />
Matters and Interactions: 4th Edition <br><br />
WebAssign <br><br />
College Physics: Ninth Edition by Raymond Serway and Chris Vuille <br><br />
[[Category:Angular Momentum]]</div>Nvohra3http://www.physicsbook.gatech.edu/index.php?title=Systems_with_Nonzero_Torque&diff=19813Systems with Nonzero Torque2015-12-06T04:44:17Z<p>Nvohra3: /* A Mathematical Model */</p>
<hr />
<div>In certain systems, external torques have an effect on a system's angular momentum. Since these external forces do not sum to zero, we end up with a system with non-zero net torque.<br />
<br />
==The Main Idea==<br />
<br />
With previous systems involving torque, we've been fortunate enough to have systems where the net torque is non-zero, hence <math> \vec{L}_{final} = \vec{L}_{initial}. </math> <br><br />
See systems with zero net torque in "See Also" section below for more information. <br><br />
<br />
However, we're not always fortunate enough to have such systems. In such cases, our computations become a little more complicated, and we'll see how below.<br />
<br />
===A Mathematical Model===<br />
<br />
The angular momentum principle is the following: <math>{\frac{d\vec{L}}{dt}}= \vec{r} * \vec{F}_{net} = \vec{т}_{net} </math> <br><br />
As previously mentioned, we'll now look at the case where <math> \vec{F}_{net} </math> is NOT equal to 0.<br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
===Simple===<br />
A constant net nonzero torque is exerted on an object. Which of the following quantities cannot be constant for this object? <br><br />
A) Moment of inertia <br><br />
B) Center of mass <br><br />
C) Angular momentum <br><br />
D) Angular velocity <br><br />
E) Angular acceleration <br><br />
<br><br />
Solution/Explanation: <br><br />
C, D. Why? <br><br />
A) Moment of inertia does not change depending on whether torque is exerted on an object; moment of inertia depends on the object and axis of rotation, nothing more. <br><br />
B) Center of mass doesn't change with applied torque as well. <br><br />
C) Angular momentum is equal to inertia times angular speed, and we establish below that angular velocity changes. <br><br />
D) Angular velocity changes since a constant force is being applied to the object, so it's speed/velocity must inherently increase. <br><br />
E) Because the torque being applied is constant, angular acceleration does not change (remember, acceleration is a measure of the rate of change of velocity!). <br><br />
<br />
===Middling===<br />
[[File:Screen Shot 2015-12-05 at 9.47.39 PM.png]]<br />
<br />
[[File:Solution.jpg]]<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
:::I had taken physics in high school, and a majority of the concepts covered in this class were familiar to me. However, I had never seen any of the material we covered in the last unit (like angular momentum, conservation of angular momentum, torque, etc.). This material was new and something I found interesting since it went a step further with the information we learned throughout the semester.<br />
#How is it connected to your major? Is there an interesting industrial application?<br />
:::My major is Computer Science, so I cannot really draw a clear line between my current coursework and this topic. That being said, physics is, of course, used in computer science. A good example would be in programming games where most interactions between objects involve physics of some kind, and the programmers/game designers want to model realistic situations in game. Another example that never really dawned upon me until about halfway through the semester was that both topics require a decent level skill in problem solving/reasoning. I've liked physics this semester because (and I guess this just applies to math in general) it's almost beautiful just to see how, in the end, everything works out and makes sense. Throughout the semester, I've never had a moment during class where I've flat out said, "No, that doesn't make sense" simply because that's never happened. I've never been a huge fan of physics, but even I can appreciate something that comes together so well.<br />
<br />
==History==<br />
<br />
This concept doesn't have it's own history since it's just a section under torque, so refer to http://www.physicsbook.gatech.edu/Torque#History for more information.<br />
<br />
== See also ==<br />
<br />
A general description of torque:<br />
http://www.physicsbook.gatech.edu/Torque<br />
<br />
===External links===<br />
[https://www.youtube.com/watch?v=mvzSjRFQbHE A brief overview on systems with non-zero torque]<br />
<br />
==References==<br />
<br />
Matters and Interactions: 4th Edition <br><br />
WebAssign <br><br />
College Physics: Ninth Edition by Raymond Serway and Chris Vuille <br><br />
[[Category:Angular Momentum]]</div>Nvohra3http://www.physicsbook.gatech.edu/index.php?title=Systems_with_Nonzero_Torque&diff=19809Systems with Nonzero Torque2015-12-06T04:43:55Z<p>Nvohra3: /* A Mathematical Model */</p>
<hr />
<div>In certain systems, external torques have an effect on a system's angular momentum. Since these external forces do not sum to zero, we end up with a system with non-zero net torque.<br />
<br />
==The Main Idea==<br />
<br />
With previous systems involving torque, we've been fortunate enough to have systems where the net torque is non-zero, hence <math> \vec{L}_{final} = \vec{L}_{initial}. </math> <br><br />
See systems with zero net torque in "See Also" section below for more information. <br><br />
<br />
However, we're not always fortunate enough to have such systems. In such cases, our computations become a little more complicated, and we'll see how below.<br />
<br />
===A Mathematical Model===<br />
<br />
The angular momentum principle is the following: <math>{\frac{d\vec{L}}{dt}}= \vec{r} * \vec{F}_{net} = \vec{т}_{net} </math> <br><br />
As previously mentioned, we'll now look at the case where \vec{F}_{net} is NOT equal to 0.<br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
===Simple===<br />
A constant net nonzero torque is exerted on an object. Which of the following quantities cannot be constant for this object? <br><br />
A) Moment of inertia <br><br />
B) Center of mass <br><br />
C) Angular momentum <br><br />
D) Angular velocity <br><br />
E) Angular acceleration <br><br />
<br><br />
Solution/Explanation: <br><br />
C, D. Why? <br><br />
A) Moment of inertia does not change depending on whether torque is exerted on an object; moment of inertia depends on the object and axis of rotation, nothing more. <br><br />
B) Center of mass doesn't change with applied torque as well. <br><br />
C) Angular momentum is equal to inertia times angular speed, and we establish below that angular velocity changes. <br><br />
D) Angular velocity changes since a constant force is being applied to the object, so it's speed/velocity must inherently increase. <br><br />
E) Because the torque being applied is constant, angular acceleration does not change (remember, acceleration is a measure of the rate of change of velocity!). <br><br />
<br />
===Middling===<br />
[[File:Screen Shot 2015-12-05 at 9.47.39 PM.png]]<br />
<br />
[[File:Solution.jpg]]<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
:::I had taken physics in high school, and a majority of the concepts covered in this class were familiar to me. However, I had never seen any of the material we covered in the last unit (like angular momentum, conservation of angular momentum, torque, etc.). This material was new and something I found interesting since it went a step further with the information we learned throughout the semester.<br />
#How is it connected to your major? Is there an interesting industrial application?<br />
:::My major is Computer Science, so I cannot really draw a clear line between my current coursework and this topic. That being said, physics is, of course, used in computer science. A good example would be in programming games where most interactions between objects involve physics of some kind, and the programmers/game designers want to model realistic situations in game. Another example that never really dawned upon me until about halfway through the semester was that both topics require a decent level skill in problem solving/reasoning. I've liked physics this semester because (and I guess this just applies to math in general) it's almost beautiful just to see how, in the end, everything works out and makes sense. Throughout the semester, I've never had a moment during class where I've flat out said, "No, that doesn't make sense" simply because that's never happened. I've never been a huge fan of physics, but even I can appreciate something that comes together so well.<br />
<br />
==History==<br />
<br />
This concept doesn't have it's own history since it's just a section under torque, so refer to http://www.physicsbook.gatech.edu/Torque#History for more information.<br />
<br />
== See also ==<br />
<br />
A general description of torque:<br />
http://www.physicsbook.gatech.edu/Torque<br />
<br />
===External links===<br />
[https://www.youtube.com/watch?v=mvzSjRFQbHE A brief overview on systems with non-zero torque]<br />
<br />
==References==<br />
<br />
Matters and Interactions: 4th Edition <br><br />
WebAssign <br><br />
College Physics: Ninth Edition by Raymond Serway and Chris Vuille <br><br />
[[Category:Angular Momentum]]</div>Nvohra3http://www.physicsbook.gatech.edu/index.php?title=Systems_with_Nonzero_Torque&diff=19650Systems with Nonzero Torque2015-12-06T04:30:19Z<p>Nvohra3: </p>
<hr />
<div>In certain systems, external torques have an effect on a system's angular momentum. Since these external forces do not sum to zero, we end up with a system with non-zero net torque.<br />
<br />
==The Main Idea==<br />
<br />
With previous systems involving torque, we've been fortunate enough to have systems where the net torque is non-zero, hence <math> \vec{L}_{final} = \vec{L}_{initial}. </math> <br><br />
See systems with zero net torque in "See Also" section below for more information. <br><br />
<br />
However, we're not always fortunate enough to have such systems. In such cases, our computations become a little more complicated, and we'll see how below.<br />
<br />
===A Mathematical Model===<br />
<br />
So the angular momentum principle is the following: <math>{\frac{d\vec{L}}{dt}}= \vec{r} * \vec{F}_{net} = \vec{т}_{net} </math><br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
===Simple===<br />
A constant net nonzero torque is exerted on an object. Which of the following quantities cannot be constant for this object? <br><br />
A) Moment of inertia <br><br />
B) Center of mass <br><br />
C) Angular momentum <br><br />
D) Angular velocity <br><br />
E) Angular acceleration <br><br />
<br><br />
Solution/Explanation: <br><br />
C, D. Why? <br><br />
A) Moment of inertia does not change depending on whether torque is exerted on an object; moment of inertia depends on the object and axis of rotation, nothing more. <br><br />
B) Center of mass doesn't change with applied torque as well. <br><br />
C) Angular momentum is equal to inertia times angular speed, and we establish below that angular velocity changes. <br><br />
D) Angular velocity changes since a constant force is being applied to the object, so it's speed/velocity must inherently increase. <br><br />
E) Because the torque being applied is constant, angular acceleration does not change (remember, acceleration is a measure of the rate of change of velocity!). <br><br />
<br />
===Middling===<br />
[[File:Screen Shot 2015-12-05 at 9.47.39 PM.png]]<br />
<br />
[[File:Solution.jpg]]<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
:::I had taken physics in high school, and a majority of the concepts covered in this class were familiar to me. However, I had never seen any of the material we covered in the last unit (like angular momentum, conservation of angular momentum, torque, etc.). This material was new and something I found interesting since it went a step further with the information we learned throughout the semester.<br />
#How is it connected to your major? Is there an interesting industrial application?<br />
:::My major is Computer Science, so I cannot really draw a clear line between my current coursework and this topic. That being said, physics is, of course, used in computer science. A good example would be in programming games where most interactions between objects involve physics of some kind, and the programmers/game designers want to model realistic situations in game. Another example that never really dawned upon me until about halfway through the semester was that both topics require a decent level skill in problem solving/reasoning. I've liked physics this semester because (and I guess this just applies to math in general) it's almost beautiful just to see how, in the end, everything works out and makes sense. Throughout the semester, I've never had a moment during class where I've flat out said, "No, that doesn't make sense" simply because that's never happened. I've never been a huge fan of physics, but even I can appreciate something that comes together so well.<br />
<br />
==History==<br />
<br />
This concept doesn't have it's own history since it's just a section under torque, so refer to http://www.physicsbook.gatech.edu/Torque#History for more information.<br />
<br />
== See also ==<br />
<br />
A general description of torque:<br />
http://www.physicsbook.gatech.edu/Torque<br />
<br />
===External links===<br />
[https://www.youtube.com/watch?v=mvzSjRFQbHE A brief overview on systems with non-zero torque]<br />
<br />
==References==<br />
<br />
Matters and Interactions: 4th Edition <br><br />
WebAssign <br><br />
College Physics: Ninth Edition by Raymond Serway and Chris Vuille <br><br />
[[Category:Angular Momentum]]</div>Nvohra3http://www.physicsbook.gatech.edu/index.php?title=Systems_with_Nonzero_Torque&diff=19423Systems with Nonzero Torque2015-12-06T04:08:10Z<p>Nvohra3: /* External links */</p>
<hr />
<div>In certain systems, external torques have an effect on a system's angular momentum. Since these external forces do not sum to zero, we end up with a system with nonzero torque.<br />
<br />
==The Main Idea==<br />
<br />
With previous systems involving torque, we've been fortunate enough to have systems where the net torque is non-zero, hence <math> \vec{L}_{final} = \vec{L}_{initial}. </math> <br><br />
See systems with zero net torque in "See Also" section below for more information. <br><br />
<br />
However, we're not always fortunate enough to have such systems. In such cases, our computations become a little more complicated, and we'll see how below.<br />
<br />
===A Mathematical Model===<br />
<br />
So the angular momentum principle is the following: <math>{\frac{d\vec{L}}{dt}}= \vec{r} * \vec{F}_{net} = \vec{т}_{net} </math><br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
===Simple===<br />
A constant net nonzero torque is exerted on an object. Which of the following quantities cannot be constant for this object? <br><br />
A) Moment of inertia <br><br />
B) Center of mass <br><br />
C) Angular momentum <br><br />
D) Angular velocity <br><br />
E) Angular acceleration <br><br />
<br><br />
Solution/Explanation: <br><br />
C, D. Why? <br><br />
A) Moment of inertia does not change depending on whether torque is exerted on an object; moment of inertia depends on the object and axis of rotation, nothing more. <br><br />
B) Center of mass doesn't change with applied torque as well. <br><br />
C) Angular momentum is equal to inertia times angular speed, and we establish below that angular velocity changes. <br><br />
D) Angular velocity changes since a constant force is being applied to the object, so it's speed/velocity must inherently increase. <br><br />
E) Because the torque being applied is constant, angular acceleration does not change (remember, acceleration is a measure of the rate of change of velocity!). <br><br />
<br />
===Middling===<br />
[[File:Screen Shot 2015-12-05 at 9.47.39 PM.png]]<br />
<br />
[[File:Solution.jpg]]<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
:::I had taken physics in high school, and a majority of the concepts covered in this class were familiar to me. However, I had never seen any of the material we covered in the last unit (like angular momentum, conservation of angular momentum, torque, etc.). This material was new and something I found interesting since it went a step further with the information we learned throughout the semester.<br />
#How is it connected to your major? Is there an interesting industrial application?<br />
:::My major is Computer Science, so I cannot really draw a clear line between my current coursework and this topic. That being said, physics is, of course, used in computer science. A good example would be in programming games where most interactions between objects involve physics of some kind, and the programmers/game designers want to model realistic situations in game. Another example that never really dawned upon me until about halfway through the semester was that both topics require a decent level skill in problem solving/reasoning. I've liked physics this semester because (and I guess this just applies to math in general) it's almost beautiful just to see how, in the end, everything works out and makes sense. Throughout the semester, I've never had a moment during class where I've flat out said, "No, that doesn't make sense" simply because that's never happened. I've never been a huge fan of physics, but even I can appreciate something that comes together so well.<br />
<br />
==History==<br />
<br />
This concept doesn't have it's own history since it's just a section under torque, so refer to http://www.physicsbook.gatech.edu/Torque#History for more information.<br />
<br />
== See also ==<br />
<br />
A general description of torque:<br />
http://www.physicsbook.gatech.edu/Torque<br />
<br />
===External links===<br />
[https://www.youtube.com/watch?v=mvzSjRFQbHE A brief overview on systems with non-zero torque]<br />
<br />
==References==<br />
<br />
Matters and Interactions: 4th Edition <br><br />
WebAssign <br><br />
College Physics: Ninth Edition by Raymond Serway and Chris Vuille <br><br />
[[Category:Angular Momentum]]</div>Nvohra3http://www.physicsbook.gatech.edu/index.php?title=Systems_with_Nonzero_Torque&diff=19417Systems with Nonzero Torque2015-12-06T04:07:41Z<p>Nvohra3: /* External links */</p>
<hr />
<div>In certain systems, external torques have an effect on a system's angular momentum. Since these external forces do not sum to zero, we end up with a system with nonzero torque.<br />
<br />
==The Main Idea==<br />
<br />
With previous systems involving torque, we've been fortunate enough to have systems where the net torque is non-zero, hence <math> \vec{L}_{final} = \vec{L}_{initial}. </math> <br><br />
See systems with zero net torque in "See Also" section below for more information. <br><br />
<br />
However, we're not always fortunate enough to have such systems. In such cases, our computations become a little more complicated, and we'll see how below.<br />
<br />
===A Mathematical Model===<br />
<br />
So the angular momentum principle is the following: <math>{\frac{d\vec{L}}{dt}}= \vec{r} * \vec{F}_{net} = \vec{т}_{net} </math><br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
===Simple===<br />
A constant net nonzero torque is exerted on an object. Which of the following quantities cannot be constant for this object? <br><br />
A) Moment of inertia <br><br />
B) Center of mass <br><br />
C) Angular momentum <br><br />
D) Angular velocity <br><br />
E) Angular acceleration <br><br />
<br><br />
Solution/Explanation: <br><br />
C, D. Why? <br><br />
A) Moment of inertia does not change depending on whether torque is exerted on an object; moment of inertia depends on the object and axis of rotation, nothing more. <br><br />
B) Center of mass doesn't change with applied torque as well. <br><br />
C) Angular momentum is equal to inertia times angular speed, and we establish below that angular velocity changes. <br><br />
D) Angular velocity changes since a constant force is being applied to the object, so it's speed/velocity must inherently increase. <br><br />
E) Because the torque being applied is constant, angular acceleration does not change (remember, acceleration is a measure of the rate of change of velocity!). <br><br />
<br />
===Middling===<br />
[[File:Screen Shot 2015-12-05 at 9.47.39 PM.png]]<br />
<br />
[[File:Solution.jpg]]<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
:::I had taken physics in high school, and a majority of the concepts covered in this class were familiar to me. However, I had never seen any of the material we covered in the last unit (like angular momentum, conservation of angular momentum, torque, etc.). This material was new and something I found interesting since it went a step further with the information we learned throughout the semester.<br />
#How is it connected to your major? Is there an interesting industrial application?<br />
:::My major is Computer Science, so I cannot really draw a clear line between my current coursework and this topic. That being said, physics is, of course, used in computer science. A good example would be in programming games where most interactions between objects involve physics of some kind, and the programmers/game designers want to model realistic situations in game. Another example that never really dawned upon me until about halfway through the semester was that both topics require a decent level skill in problem solving/reasoning. I've liked physics this semester because (and I guess this just applies to math in general) it's almost beautiful just to see how, in the end, everything works out and makes sense. Throughout the semester, I've never had a moment during class where I've flat out said, "No, that doesn't make sense" simply because that's never happened. I've never been a huge fan of physics, but even I can appreciate something that comes together so well.<br />
<br />
==History==<br />
<br />
This concept doesn't have it's own history since it's just a section under torque, so refer to http://www.physicsbook.gatech.edu/Torque#History for more information.<br />
<br />
== See also ==<br />
<br />
A general description of torque:<br />
http://www.physicsbook.gatech.edu/Torque<br />
<br />
===External links===<br />
A brief overview on the topic: [https://www.youtube.com/watch?v=mvzSjRFQbHE Test]<br />
<br />
==References==<br />
<br />
Matters and Interactions: 4th Edition <br><br />
WebAssign <br><br />
College Physics: Ninth Edition by Raymond Serway and Chris Vuille <br><br />
[[Category:Angular Momentum]]</div>Nvohra3http://www.physicsbook.gatech.edu/index.php?title=Systems_with_Nonzero_Torque&diff=19396Systems with Nonzero Torque2015-12-06T04:06:10Z<p>Nvohra3: /* Simple */</p>
<hr />
<div>In certain systems, external torques have an effect on a system's angular momentum. Since these external forces do not sum to zero, we end up with a system with nonzero torque.<br />
<br />
==The Main Idea==<br />
<br />
With previous systems involving torque, we've been fortunate enough to have systems where the net torque is non-zero, hence <math> \vec{L}_{final} = \vec{L}_{initial}. </math> <br><br />
See systems with zero net torque in "See Also" section below for more information. <br><br />
<br />
However, we're not always fortunate enough to have such systems. In such cases, our computations become a little more complicated, and we'll see how below.<br />
<br />
===A Mathematical Model===<br />
<br />
So the angular momentum principle is the following: <math>{\frac{d\vec{L}}{dt}}= \vec{r} * \vec{F}_{net} = \vec{т}_{net} </math><br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
===Simple===<br />
A constant net nonzero torque is exerted on an object. Which of the following quantities cannot be constant for this object? <br><br />
A) Moment of inertia <br><br />
B) Center of mass <br><br />
C) Angular momentum <br><br />
D) Angular velocity <br><br />
E) Angular acceleration <br><br />
<br><br />
Solution/Explanation: <br><br />
C, D. Why? <br><br />
A) Moment of inertia does not change depending on whether torque is exerted on an object; moment of inertia depends on the object and axis of rotation, nothing more. <br><br />
B) Center of mass doesn't change with applied torque as well. <br><br />
C) Angular momentum is equal to inertia times angular speed, and we establish below that angular velocity changes. <br><br />
D) Angular velocity changes since a constant force is being applied to the object, so it's speed/velocity must inherently increase. <br><br />
E) Because the torque being applied is constant, angular acceleration does not change (remember, acceleration is a measure of the rate of change of velocity!). <br><br />
<br />
===Middling===<br />
[[File:Screen Shot 2015-12-05 at 9.47.39 PM.png]]<br />
<br />
[[File:Solution.jpg]]<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
:::I had taken physics in high school, and a majority of the concepts covered in this class were familiar to me. However, I had never seen any of the material we covered in the last unit (like angular momentum, conservation of angular momentum, torque, etc.). This material was new and something I found interesting since it went a step further with the information we learned throughout the semester.<br />
#How is it connected to your major? Is there an interesting industrial application?<br />
:::My major is Computer Science, so I cannot really draw a clear line between my current coursework and this topic. That being said, physics is, of course, used in computer science. A good example would be in programming games where most interactions between objects involve physics of some kind, and the programmers/game designers want to model realistic situations in game. Another example that never really dawned upon me until about halfway through the semester was that both topics require a decent level skill in problem solving/reasoning. I've liked physics this semester because (and I guess this just applies to math in general) it's almost beautiful just to see how, in the end, everything works out and makes sense. Throughout the semester, I've never had a moment during class where I've flat out said, "No, that doesn't make sense" simply because that's never happened. I've never been a huge fan of physics, but even I can appreciate something that comes together so well.<br />
<br />
==History==<br />
<br />
This concept doesn't have it's own history since it's just a section under torque, so refer to http://www.physicsbook.gatech.edu/Torque#History for more information.<br />
<br />
== See also ==<br />
<br />
A general description of torque:<br />
http://www.physicsbook.gatech.edu/Torque<br />
<br />
===External links===<br />
A brief overview on the topic: [https://www.youtube.com/watch?v=mvzSjRFQbHE]<br />
<br />
==References==<br />
<br />
Matters and Interactions: 4th Edition <br><br />
WebAssign <br><br />
College Physics: Ninth Edition by Raymond Serway and Chris Vuille <br><br />
[[Category:Angular Momentum]]</div>Nvohra3http://www.physicsbook.gatech.edu/index.php?title=Systems_with_Nonzero_Torque&diff=19381Systems with Nonzero Torque2015-12-06T04:03:24Z<p>Nvohra3: /* Simple */</p>
<hr />
<div>Claimed by nvohra3.<br />
<br />
In certain systems, external torques have an effect on a system's angular momentum. Since these external forces do not sum to zero, we end up with a system with nonzero torque.<br />
<br />
==The Main Idea==<br />
<br />
With previous systems involving torque, we've been fortunate enough to have systems where the net torque is non-zero, hence <math> \vec{L}_{final} = \vec{L}_{initial}. </math> <br><br />
See systems with zero net torque in "See Also" section below for more information. <br><br />
<br />
However, we're not always fortunate enough to have such systems. In such cases, our computations become a little more complicated, and we'll see how below.<br />
<br />
===A Mathematical Model===<br />
<br />
So the angular momentum principle is the following: <math>{\frac{d\vec{L}}{dt}}= \vec{r} * \vec{F}_{net} = \vec{т}_{net} </math><br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
===Simple===<br />
A constant net nonzero torque is exerted on an object. Which of the following quantities cannot be constant for this object? <br><br />
A) Moment of inertia <br><br />
B) Center of mass <br><br />
C) Angular momentum <br><br />
D) Angular velocity <br><br />
E) Angular acceleration <br><br />
<br><br />
Answer below.<br />
<br><br />
Solution/Explanation: <br><br />
C, D. Why? <br><br />
A) Moment of inertia does not change depending on whether torque is exerted on an object; moment of inertia depends on the object and axis of rotation, nothing more. <br><br />
B) Center of mass doesn't change with applied torque as well. <br><br />
C) Angular momentum is equal to inertia times angular speed, and we establish below that angular velocity changes. <br><br />
D) Angular velocity changes since a constant force is being applied to the object, so it's speed/velocity must inherently increase. <br><br />
E) Because the torque being applied is constant, angular acceleration does not change (remember, acceleration is a measure of the rate of change of velocity!). <br><br />
<br />
===Middling===<br />
[[File:Screen Shot 2015-12-05 at 9.47.39 PM.png]]<br />
<br />
[[File:Solution.jpg]]<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
:::I had taken physics in high school, and a majority of the concepts covered in this class were familiar to me. However, I had never seen any of the material we covered in the last unit (like angular momentum, conservation of angular momentum, torque, etc.). This material was new and something I found interesting since it went a step further with the information we learned throughout the semester.<br />
#How is it connected to your major? Is there an interesting industrial application?<br />
:::My major is Computer Science, so I cannot really draw a clear line between my current coursework and this topic. That being said, physics is, of course, used in computer science. A good example would be in programming games where most interactions between objects involve physics of some kind, and the programmers/game designers want to model realistic situations in game. Another example that never really dawned upon me until about halfway through the semester was that both topics require a decent level skill in problem solving/reasoning. I've liked physics this semester because (and I guess this just applies to math in general) it's almost beautiful just to see how, in the end, everything works out and makes sense. Throughout the semester, I've never had a moment during class where I've flat out said, "No, that doesn't make sense" simply because that's never happened. I've never been a huge fan of physics, but even I can appreciate something that comes together so well.<br />
<br />
==History==<br />
<br />
This concept doesn't have it's own history since it's just a section under torque, so refer to http://www.physicsbook.gatech.edu/Torque#History for more information.<br />
<br />
== See also ==<br />
<br />
A general description of torque:<br />
http://www.physicsbook.gatech.edu/Torque<br />
<br />
===External links===<br />
A brief overview on the topic: [https://www.youtube.com/watch?v=mvzSjRFQbHE]<br />
<br />
==References==<br />
<br />
Matters and Interactions: 4th Edition <br><br />
WebAssign <br><br />
College Physics: Ninth Edition by Raymond Serway and Chris Vuille <br><br />
[[Category:Angular Momentum]]</div>Nvohra3http://www.physicsbook.gatech.edu/index.php?title=Systems_with_Nonzero_Torque&diff=19376Systems with Nonzero Torque2015-12-06T04:02:43Z<p>Nvohra3: /* Examples */</p>
<hr />
<div>Claimed by nvohra3.<br />
<br />
In certain systems, external torques have an effect on a system's angular momentum. Since these external forces do not sum to zero, we end up with a system with nonzero torque.<br />
<br />
==The Main Idea==<br />
<br />
With previous systems involving torque, we've been fortunate enough to have systems where the net torque is non-zero, hence <math> \vec{L}_{final} = \vec{L}_{initial}. </math> <br><br />
See systems with zero net torque in "See Also" section below for more information. <br><br />
<br />
However, we're not always fortunate enough to have such systems. In such cases, our computations become a little more complicated, and we'll see how below.<br />
<br />
===A Mathematical Model===<br />
<br />
So the angular momentum principle is the following: <math>{\frac{d\vec{L}}{dt}}= \vec{r} * \vec{F}_{net} = \vec{т}_{net} </math><br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
===Simple===<br />
A constant net nonzero torque is exerted on an object. Which of the following quantities cannot be constant for this object? <br><br />
A) Moment of inertia <br><br />
B) Center of mass <br><br />
C) Angular momentum <br><br />
D) Angular velocity <br><br />
E) Angular acceleration <br><br />
<br><br />
Solution/Explanation: <br><br />
C, D. Why? <br><br />
A) Moment of inertia does not change depending on whether torque is exerted on an object; moment of inertia depends on the object and axis of rotation, nothing more. <br><br />
B) Center of mass doesn't change with applied torque as well. <br><br />
C) Angular momentum is equal to inertia times angular speed, and we establish below that angular velocity changes. <br><br />
D) Angular velocity changes since a constant force is being applied to the object, so it's speed/velocity must inherently increase. <br><br />
E) Because the torque being applied is constant, angular acceleration does not change (remember, acceleration is a measure of the rate of change of velocity!). <br><br />
<br />
===Middling===<br />
[[File:Screen Shot 2015-12-05 at 9.47.39 PM.png]]<br />
<br />
[[File:Solution.jpg]]<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
:::I had taken physics in high school, and a majority of the concepts covered in this class were familiar to me. However, I had never seen any of the material we covered in the last unit (like angular momentum, conservation of angular momentum, torque, etc.). This material was new and something I found interesting since it went a step further with the information we learned throughout the semester.<br />
#How is it connected to your major? Is there an interesting industrial application?<br />
:::My major is Computer Science, so I cannot really draw a clear line between my current coursework and this topic. That being said, physics is, of course, used in computer science. A good example would be in programming games where most interactions between objects involve physics of some kind, and the programmers/game designers want to model realistic situations in game. Another example that never really dawned upon me until about halfway through the semester was that both topics require a decent level skill in problem solving/reasoning. I've liked physics this semester because (and I guess this just applies to math in general) it's almost beautiful just to see how, in the end, everything works out and makes sense. Throughout the semester, I've never had a moment during class where I've flat out said, "No, that doesn't make sense" simply because that's never happened. I've never been a huge fan of physics, but even I can appreciate something that comes together so well.<br />
<br />
==History==<br />
<br />
This concept doesn't have it's own history since it's just a section under torque, so refer to http://www.physicsbook.gatech.edu/Torque#History for more information.<br />
<br />
== See also ==<br />
<br />
A general description of torque:<br />
http://www.physicsbook.gatech.edu/Torque<br />
<br />
===External links===<br />
A brief overview on the topic: [https://www.youtube.com/watch?v=mvzSjRFQbHE]<br />
<br />
==References==<br />
<br />
Matters and Interactions: 4th Edition <br><br />
WebAssign <br><br />
College Physics: Ninth Edition by Raymond Serway and Chris Vuille <br><br />
[[Category:Angular Momentum]]</div>Nvohra3http://www.physicsbook.gatech.edu/index.php?title=Systems_with_Nonzero_Torque&diff=19373Systems with Nonzero Torque2015-12-06T04:02:18Z<p>Nvohra3: /* Connectedness */</p>
<hr />
<div>Claimed by nvohra3.<br />
<br />
In certain systems, external torques have an effect on a system's angular momentum. Since these external forces do not sum to zero, we end up with a system with nonzero torque.<br />
<br />
==The Main Idea==<br />
<br />
With previous systems involving torque, we've been fortunate enough to have systems where the net torque is non-zero, hence <math> \vec{L}_{final} = \vec{L}_{initial}. </math> <br><br />
See systems with zero net torque in "See Also" section below for more information. <br><br />
<br />
However, we're not always fortunate enough to have such systems. In such cases, our computations become a little more complicated, and we'll see how below.<br />
<br />
===A Mathematical Model===<br />
<br />
So the angular momentum principle is the following: <math>{\frac{d\vec{L}}{dt}}= \vec{r} * \vec{F}_{net} = \vec{т}_{net} </math><br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Taken from sources listed at bottom of page.<br />
<br />
===Simple===<br />
A constant net nonzero torque is exerted on an object. Which of the following quantities cannot be constant for this object? <br><br />
A) Moment of inertia <br><br />
B) Center of mass <br><br />
C) Angular momentum <br><br />
D) Angular velocity <br><br />
E) Angular acceleration <br><br />
<br><br />
Solution/Explanation: <br><br />
C, D. Why? <br><br />
A) Moment of inertia does not change depending on whether torque is exerted on an object; moment of inertia depends on the object and axis of rotation, nothing more. <br><br />
B) Center of mass doesn't change with applied torque as well. <br><br />
C) Angular momentum is equal to inertia times angular speed, and we establish below that angular velocity changes. <br><br />
D) Angular velocity changes since a constant force is being applied to the object, so it's speed/velocity must inherently increase. <br><br />
E) Because the torque being applied is constant, angular acceleration does not change (remember, acceleration is a measure of the rate of change of velocity!). <br><br />
<br />
===Middling===<br />
[[File:Screen Shot 2015-12-05 at 9.47.39 PM.png]]<br />
<br />
[[File:Solution.jpg]]<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
:::I had taken physics in high school, and a majority of the concepts covered in this class were familiar to me. However, I had never seen any of the material we covered in the last unit (like angular momentum, conservation of angular momentum, torque, etc.). This material was new and something I found interesting since it went a step further with the information we learned throughout the semester.<br />
#How is it connected to your major? Is there an interesting industrial application?<br />
:::My major is Computer Science, so I cannot really draw a clear line between my current coursework and this topic. That being said, physics is, of course, used in computer science. A good example would be in programming games where most interactions between objects involve physics of some kind, and the programmers/game designers want to model realistic situations in game. Another example that never really dawned upon me until about halfway through the semester was that both topics require a decent level skill in problem solving/reasoning. I've liked physics this semester because (and I guess this just applies to math in general) it's almost beautiful just to see how, in the end, everything works out and makes sense. Throughout the semester, I've never had a moment during class where I've flat out said, "No, that doesn't make sense" simply because that's never happened. I've never been a huge fan of physics, but even I can appreciate something that comes together so well.<br />
<br />
==History==<br />
<br />
This concept doesn't have it's own history since it's just a section under torque, so refer to http://www.physicsbook.gatech.edu/Torque#History for more information.<br />
<br />
== See also ==<br />
<br />
A general description of torque:<br />
http://www.physicsbook.gatech.edu/Torque<br />
<br />
===External links===<br />
A brief overview on the topic: [https://www.youtube.com/watch?v=mvzSjRFQbHE]<br />
<br />
==References==<br />
<br />
Matters and Interactions: 4th Edition <br><br />
WebAssign <br><br />
College Physics: Ninth Edition by Raymond Serway and Chris Vuille <br><br />
[[Category:Angular Momentum]]</div>Nvohra3http://www.physicsbook.gatech.edu/index.php?title=Systems_with_Nonzero_Torque&diff=19269Systems with Nonzero Torque2015-12-06T03:49:09Z<p>Nvohra3: /* Connectedness */</p>
<hr />
<div>Claimed by nvohra3.<br />
<br />
In certain systems, external torques have an effect on a system's angular momentum. Since these external forces do not sum to zero, we end up with a system with nonzero torque.<br />
<br />
==The Main Idea==<br />
<br />
With previous systems involving torque, we've been fortunate enough to have systems where the net torque is non-zero, hence <math> \vec{L}_{final} = \vec{L}_{initial}. </math> <br><br />
See systems with zero net torque in "See Also" section below for more information. <br><br />
<br />
However, we're not always fortunate enough to have such systems. In such cases, our computations become a little more complicated, and we'll see how below.<br />
<br />
===A Mathematical Model===<br />
<br />
So the angular momentum principle is the following: <math>{\frac{d\vec{L}}{dt}}= \vec{r} * \vec{F}_{net} = \vec{т}_{net} </math><br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Taken from sources listed at bottom of page.<br />
<br />
===Simple===<br />
A constant net nonzero torque is exerted on an object. Which of the following quantities cannot be constant for this object? <br><br />
A) Moment of inertia <br><br />
B) Center of mass <br><br />
C) Angular momentum <br><br />
D) Angular velocity <br><br />
E) Angular acceleration <br><br />
<br><br />
Solution/Explanation: <br><br />
C, D. Why? <br><br />
A) Moment of inertia does not change depending on whether torque is exerted on an object; moment of inertia depends on the object and axis of rotation, nothing more. <br><br />
B) Center of mass doesn't change with applied torque as well. <br><br />
C) Angular momentum is equal to inertia times angular speed, and we establish below that angular velocity changes. <br><br />
D) Angular velocity changes since a constant force is being applied to the object, so it's speed/velocity must inherently increase. <br><br />
E) Because the torque being applied is constant, angular acceleration does not change (remember, acceleration is a measure of the rate of change of velocity!). <br><br />
<br />
===Middling===<br />
[[File:Screen Shot 2015-12-05 at 9.47.39 PM.png]]<br />
<br />
[[File:Solution.jpg]]<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
::: test<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
This concept doesn't have it's own history since it's just a section under torque, so refer to http://www.physicsbook.gatech.edu/Torque#History for more information.<br />
<br />
== See also ==<br />
<br />
A general description of torque:<br />
http://www.physicsbook.gatech.edu/Torque<br />
<br />
===External links===<br />
A brief overview on the topic: [https://www.youtube.com/watch?v=mvzSjRFQbHE]<br />
<br />
==References==<br />
<br />
Matters and Interactions: 4th Edition <br><br />
WebAssign <br><br />
College Physics: Ninth Edition by Raymond Serway and Chris Vuille <br><br />
[[Category:Angular Momentum]]</div>Nvohra3http://www.physicsbook.gatech.edu/index.php?title=Systems_with_Nonzero_Torque&diff=19264Systems with Nonzero Torque2015-12-06T03:48:52Z<p>Nvohra3: /* Connectedness */</p>
<hr />
<div>Claimed by nvohra3.<br />
<br />
In certain systems, external torques have an effect on a system's angular momentum. Since these external forces do not sum to zero, we end up with a system with nonzero torque.<br />
<br />
==The Main Idea==<br />
<br />
With previous systems involving torque, we've been fortunate enough to have systems where the net torque is non-zero, hence <math> \vec{L}_{final} = \vec{L}_{initial}. </math> <br><br />
See systems with zero net torque in "See Also" section below for more information. <br><br />
<br />
However, we're not always fortunate enough to have such systems. In such cases, our computations become a little more complicated, and we'll see how below.<br />
<br />
===A Mathematical Model===<br />
<br />
So the angular momentum principle is the following: <math>{\frac{d\vec{L}}{dt}}= \vec{r} * \vec{F}_{net} = \vec{т}_{net} </math><br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Taken from sources listed at bottom of page.<br />
<br />
===Simple===<br />
A constant net nonzero torque is exerted on an object. Which of the following quantities cannot be constant for this object? <br><br />
A) Moment of inertia <br><br />
B) Center of mass <br><br />
C) Angular momentum <br><br />
D) Angular velocity <br><br />
E) Angular acceleration <br><br />
<br><br />
Solution/Explanation: <br><br />
C, D. Why? <br><br />
A) Moment of inertia does not change depending on whether torque is exerted on an object; moment of inertia depends on the object and axis of rotation, nothing more. <br><br />
B) Center of mass doesn't change with applied torque as well. <br><br />
C) Angular momentum is equal to inertia times angular speed, and we establish below that angular velocity changes. <br><br />
D) Angular velocity changes since a constant force is being applied to the object, so it's speed/velocity must inherently increase. <br><br />
E) Because the torque being applied is constant, angular acceleration does not change (remember, acceleration is a measure of the rate of change of velocity!). <br><br />
<br />
===Middling===<br />
[[File:Screen Shot 2015-12-05 at 9.47.39 PM.png]]<br />
<br />
[[File:Solution.jpg]]<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
: test<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
This concept doesn't have it's own history since it's just a section under torque, so refer to http://www.physicsbook.gatech.edu/Torque#History for more information.<br />
<br />
== See also ==<br />
<br />
A general description of torque:<br />
http://www.physicsbook.gatech.edu/Torque<br />
<br />
===External links===<br />
A brief overview on the topic: [https://www.youtube.com/watch?v=mvzSjRFQbHE]<br />
<br />
==References==<br />
<br />
Matters and Interactions: 4th Edition <br><br />
WebAssign <br><br />
College Physics: Ninth Edition by Raymond Serway and Chris Vuille <br><br />
[[Category:Angular Momentum]]</div>Nvohra3http://www.physicsbook.gatech.edu/index.php?title=Systems_with_Nonzero_Torque&diff=19254Systems with Nonzero Torque2015-12-06T03:47:52Z<p>Nvohra3: /* Connectedness */</p>
<hr />
<div>Claimed by nvohra3.<br />
<br />
In certain systems, external torques have an effect on a system's angular momentum. Since these external forces do not sum to zero, we end up with a system with nonzero torque.<br />
<br />
==The Main Idea==<br />
<br />
With previous systems involving torque, we've been fortunate enough to have systems where the net torque is non-zero, hence <math> \vec{L}_{final} = \vec{L}_{initial}. </math> <br><br />
See systems with zero net torque in "See Also" section below for more information. <br><br />
<br />
However, we're not always fortunate enough to have such systems. In such cases, our computations become a little more complicated, and we'll see how below.<br />
<br />
===A Mathematical Model===<br />
<br />
So the angular momentum principle is the following: <math>{\frac{d\vec{L}}{dt}}= \vec{r} * \vec{F}_{net} = \vec{т}_{net} </math><br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Taken from sources listed at bottom of page.<br />
<br />
===Simple===<br />
A constant net nonzero torque is exerted on an object. Which of the following quantities cannot be constant for this object? <br><br />
A) Moment of inertia <br><br />
B) Center of mass <br><br />
C) Angular momentum <br><br />
D) Angular velocity <br><br />
E) Angular acceleration <br><br />
<br><br />
Solution/Explanation: <br><br />
C, D. Why? <br><br />
A) Moment of inertia does not change depending on whether torque is exerted on an object; moment of inertia depends on the object and axis of rotation, nothing more. <br><br />
B) Center of mass doesn't change with applied torque as well. <br><br />
C) Angular momentum is equal to inertia times angular speed, and we establish below that angular velocity changes. <br><br />
D) Angular velocity changes since a constant force is being applied to the object, so it's speed/velocity must inherently increase. <br><br />
E) Because the torque being applied is constant, angular acceleration does not change (remember, acceleration is a measure of the rate of change of velocity!). <br><br />
<br />
===Middling===<br />
[[File:Screen Shot 2015-12-05 at 9.47.39 PM.png]]<br />
<br />
[[File:Solution.jpg]]<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
; test<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
This concept doesn't have it's own history since it's just a section under torque, so refer to http://www.physicsbook.gatech.edu/Torque#History for more information.<br />
<br />
== See also ==<br />
<br />
A general description of torque:<br />
http://www.physicsbook.gatech.edu/Torque<br />
<br />
===External links===<br />
A brief overview on the topic: [https://www.youtube.com/watch?v=mvzSjRFQbHE]<br />
<br />
==References==<br />
<br />
Matters and Interactions: 4th Edition <br><br />
WebAssign <br><br />
College Physics: Ninth Edition by Raymond Serway and Chris Vuille <br><br />
[[Category:Angular Momentum]]</div>Nvohra3http://www.physicsbook.gatech.edu/index.php?title=Systems_with_Nonzero_Torque&diff=19224Systems with Nonzero Torque2015-12-06T03:44:32Z<p>Nvohra3: /* References */</p>
<hr />
<div>Claimed by nvohra3.<br />
<br />
In certain systems, external torques have an effect on a system's angular momentum. Since these external forces do not sum to zero, we end up with a system with nonzero torque.<br />
<br />
==The Main Idea==<br />
<br />
With previous systems involving torque, we've been fortunate enough to have systems where the net torque is non-zero, hence <math> \vec{L}_{final} = \vec{L}_{initial}. </math> <br><br />
See systems with zero net torque in "See Also" section below for more information. <br><br />
<br />
However, we're not always fortunate enough to have such systems. In such cases, our computations become a little more complicated, and we'll see how below.<br />
<br />
===A Mathematical Model===<br />
<br />
So the angular momentum principle is the following: <math>{\frac{d\vec{L}}{dt}}= \vec{r} * \vec{F}_{net} = \vec{т}_{net} </math><br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Taken from sources listed at bottom of page.<br />
<br />
===Simple===<br />
A constant net nonzero torque is exerted on an object. Which of the following quantities cannot be constant for this object? <br><br />
A) Moment of inertia <br><br />
B) Center of mass <br><br />
C) Angular momentum <br><br />
D) Angular velocity <br><br />
E) Angular acceleration <br><br />
<br><br />
Solution/Explanation: <br><br />
C, D. Why? <br><br />
A) Moment of inertia does not change depending on whether torque is exerted on an object; moment of inertia depends on the object and axis of rotation, nothing more. <br><br />
B) Center of mass doesn't change with applied torque as well. <br><br />
C) Angular momentum is equal to inertia times angular speed, and we establish below that angular velocity changes. <br><br />
D) Angular velocity changes since a constant force is being applied to the object, so it's speed/velocity must inherently increase. <br><br />
E) Because the torque being applied is constant, angular acceleration does not change (remember, acceleration is a measure of the rate of change of velocity!). <br><br />
<br />
===Middling===<br />
[[File:Screen Shot 2015-12-05 at 9.47.39 PM.png]]<br />
<br />
[[File:Solution.jpg]]<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
This concept doesn't have it's own history since it's just a section under torque, so refer to http://www.physicsbook.gatech.edu/Torque#History for more information.<br />
<br />
== See also ==<br />
<br />
A general description of torque:<br />
http://www.physicsbook.gatech.edu/Torque<br />
<br />
===External links===<br />
A brief overview on the topic: [https://www.youtube.com/watch?v=mvzSjRFQbHE]<br />
<br />
==References==<br />
<br />
Matters and Interactions: 4th Edition <br><br />
WebAssign <br><br />
College Physics: Ninth Edition by Raymond Serway and Chris Vuille <br><br />
[[Category:Angular Momentum]]</div>Nvohra3http://www.physicsbook.gatech.edu/index.php?title=Systems_with_Nonzero_Torque&diff=19210Systems with Nonzero Torque2015-12-06T03:43:05Z<p>Nvohra3: /* History */</p>
<hr />
<div>Claimed by nvohra3.<br />
<br />
In certain systems, external torques have an effect on a system's angular momentum. Since these external forces do not sum to zero, we end up with a system with nonzero torque.<br />
<br />
==The Main Idea==<br />
<br />
With previous systems involving torque, we've been fortunate enough to have systems where the net torque is non-zero, hence <math> \vec{L}_{final} = \vec{L}_{initial}. </math> <br><br />
See systems with zero net torque in "See Also" section below for more information. <br><br />
<br />
However, we're not always fortunate enough to have such systems. In such cases, our computations become a little more complicated, and we'll see how below.<br />
<br />
===A Mathematical Model===<br />
<br />
So the angular momentum principle is the following: <math>{\frac{d\vec{L}}{dt}}= \vec{r} * \vec{F}_{net} = \vec{т}_{net} </math><br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Taken from sources listed at bottom of page.<br />
<br />
===Simple===<br />
A constant net nonzero torque is exerted on an object. Which of the following quantities cannot be constant for this object? <br><br />
A) Moment of inertia <br><br />
B) Center of mass <br><br />
C) Angular momentum <br><br />
D) Angular velocity <br><br />
E) Angular acceleration <br><br />
<br><br />
Solution/Explanation: <br><br />
C, D. Why? <br><br />
A) Moment of inertia does not change depending on whether torque is exerted on an object; moment of inertia depends on the object and axis of rotation, nothing more. <br><br />
B) Center of mass doesn't change with applied torque as well. <br><br />
C) Angular momentum is equal to inertia times angular speed, and we establish below that angular velocity changes. <br><br />
D) Angular velocity changes since a constant force is being applied to the object, so it's speed/velocity must inherently increase. <br><br />
E) Because the torque being applied is constant, angular acceleration does not change (remember, acceleration is a measure of the rate of change of velocity!). <br><br />
<br />
===Middling===<br />
[[File:Screen Shot 2015-12-05 at 9.47.39 PM.png]]<br />
<br />
[[File:Solution.jpg]]<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
This concept doesn't have it's own history since it's just a section under torque, so refer to http://www.physicsbook.gatech.edu/Torque#History for more information.<br />
<br />
== See also ==<br />
<br />
A general description of torque:<br />
http://www.physicsbook.gatech.edu/Torque<br />
<br />
===External links===<br />
A brief overview on the topic: [https://www.youtube.com/watch?v=mvzSjRFQbHE]<br />
<br />
==References==<br />
<br />
Matters and Interactions: 4th Edition <br><br />
WebAssign <br><br />
College Physics: Ninth Edition by Raymond Serway and Chris Vuille <br><br />
[[Category:Which Category did you place this in?]]</div>Nvohra3http://www.physicsbook.gatech.edu/index.php?title=Systems_with_Nonzero_Torque&diff=19184Systems with Nonzero Torque2015-12-06T03:39:35Z<p>Nvohra3: /* Difficult */</p>
<hr />
<div>Claimed by nvohra3.<br />
<br />
In certain systems, external torques have an effect on a system's angular momentum. Since these external forces do not sum to zero, we end up with a system with nonzero torque.<br />
<br />
==The Main Idea==<br />
<br />
With previous systems involving torque, we've been fortunate enough to have systems where the net torque is non-zero, hence <math> \vec{L}_{final} = \vec{L}_{initial}. </math> <br><br />
See systems with zero net torque in "See Also" section below for more information. <br><br />
<br />
However, we're not always fortunate enough to have such systems. In such cases, our computations become a little more complicated, and we'll see how below.<br />
<br />
===A Mathematical Model===<br />
<br />
So the angular momentum principle is the following: <math>{\frac{d\vec{L}}{dt}}= \vec{r} * \vec{F}_{net} = \vec{т}_{net} </math><br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Taken from sources listed at bottom of page.<br />
<br />
===Simple===<br />
A constant net nonzero torque is exerted on an object. Which of the following quantities cannot be constant for this object? <br><br />
A) Moment of inertia <br><br />
B) Center of mass <br><br />
C) Angular momentum <br><br />
D) Angular velocity <br><br />
E) Angular acceleration <br><br />
<br><br />
Solution/Explanation: <br><br />
C, D. Why? <br><br />
A) Moment of inertia does not change depending on whether torque is exerted on an object; moment of inertia depends on the object and axis of rotation, nothing more. <br><br />
B) Center of mass doesn't change with applied torque as well. <br><br />
C) Angular momentum is equal to inertia times angular speed, and we establish below that angular velocity changes. <br><br />
D) Angular velocity changes since a constant force is being applied to the object, so it's speed/velocity must inherently increase. <br><br />
E) Because the torque being applied is constant, angular acceleration does not change (remember, acceleration is a measure of the rate of change of velocity!). <br><br />
<br />
===Middling===<br />
[[File:Screen Shot 2015-12-05 at 9.47.39 PM.png]]<br />
<br />
[[File:Solution.jpg]]<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
A general description of torque:<br />
http://www.physicsbook.gatech.edu/Torque<br />
<br />
===External links===<br />
A brief overview on the topic: [https://www.youtube.com/watch?v=mvzSjRFQbHE]<br />
<br />
==References==<br />
<br />
Matters and Interactions: 4th Edition <br><br />
WebAssign <br><br />
College Physics: Ninth Edition by Raymond Serway and Chris Vuille <br><br />
[[Category:Which Category did you place this in?]]</div>Nvohra3http://www.physicsbook.gatech.edu/index.php?title=Systems_with_Nonzero_Torque&diff=19181Systems with Nonzero Torque2015-12-06T03:39:24Z<p>Nvohra3: /* Middling */</p>
<hr />
<div>Claimed by nvohra3.<br />
<br />
In certain systems, external torques have an effect on a system's angular momentum. Since these external forces do not sum to zero, we end up with a system with nonzero torque.<br />
<br />
==The Main Idea==<br />
<br />
With previous systems involving torque, we've been fortunate enough to have systems where the net torque is non-zero, hence <math> \vec{L}_{final} = \vec{L}_{initial}. </math> <br><br />
See systems with zero net torque in "See Also" section below for more information. <br><br />
<br />
However, we're not always fortunate enough to have such systems. In such cases, our computations become a little more complicated, and we'll see how below.<br />
<br />
===A Mathematical Model===<br />
<br />
So the angular momentum principle is the following: <math>{\frac{d\vec{L}}{dt}}= \vec{r} * \vec{F}_{net} = \vec{т}_{net} </math><br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Taken from sources listed at bottom of page.<br />
<br />
===Simple===<br />
A constant net nonzero torque is exerted on an object. Which of the following quantities cannot be constant for this object? <br><br />
A) Moment of inertia <br><br />
B) Center of mass <br><br />
C) Angular momentum <br><br />
D) Angular velocity <br><br />
E) Angular acceleration <br><br />
<br><br />
Solution/Explanation: <br><br />
C, D. Why? <br><br />
A) Moment of inertia does not change depending on whether torque is exerted on an object; moment of inertia depends on the object and axis of rotation, nothing more. <br><br />
B) Center of mass doesn't change with applied torque as well. <br><br />
C) Angular momentum is equal to inertia times angular speed, and we establish below that angular velocity changes. <br><br />
D) Angular velocity changes since a constant force is being applied to the object, so it's speed/velocity must inherently increase. <br><br />
E) Because the torque being applied is constant, angular acceleration does not change (remember, acceleration is a measure of the rate of change of velocity!). <br><br />
<br />
===Middling===<br />
[[File:Screen Shot 2015-12-05 at 9.47.39 PM.png]]<br />
<br />
[[File:Solution.jpg]]<br />
<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
A general description of torque:<br />
http://www.physicsbook.gatech.edu/Torque<br />
<br />
===External links===<br />
A brief overview on the topic: [https://www.youtube.com/watch?v=mvzSjRFQbHE]<br />
<br />
==References==<br />
<br />
Matters and Interactions: 4th Edition <br><br />
WebAssign <br><br />
College Physics: Ninth Edition by Raymond Serway and Chris Vuille <br><br />
[[Category:Which Category did you place this in?]]</div>Nvohra3http://www.physicsbook.gatech.edu/index.php?title=Systems_with_Nonzero_Torque&diff=19171Systems with Nonzero Torque2015-12-06T03:38:50Z<p>Nvohra3: /* Middling */</p>
<hr />
<div>Claimed by nvohra3.<br />
<br />
In certain systems, external torques have an effect on a system's angular momentum. Since these external forces do not sum to zero, we end up with a system with nonzero torque.<br />
<br />
==The Main Idea==<br />
<br />
With previous systems involving torque, we've been fortunate enough to have systems where the net torque is non-zero, hence <math> \vec{L}_{final} = \vec{L}_{initial}. </math> <br><br />
See systems with zero net torque in "See Also" section below for more information. <br><br />
<br />
However, we're not always fortunate enough to have such systems. In such cases, our computations become a little more complicated, and we'll see how below.<br />
<br />
===A Mathematical Model===<br />
<br />
So the angular momentum principle is the following: <math>{\frac{d\vec{L}}{dt}}= \vec{r} * \vec{F}_{net} = \vec{т}_{net} </math><br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Taken from sources listed at bottom of page.<br />
<br />
===Simple===<br />
A constant net nonzero torque is exerted on an object. Which of the following quantities cannot be constant for this object? <br><br />
A) Moment of inertia <br><br />
B) Center of mass <br><br />
C) Angular momentum <br><br />
D) Angular velocity <br><br />
E) Angular acceleration <br><br />
<br><br />
Solution/Explanation: <br><br />
C, D. Why? <br><br />
A) Moment of inertia does not change depending on whether torque is exerted on an object; moment of inertia depends on the object and axis of rotation, nothing more. <br><br />
B) Center of mass doesn't change with applied torque as well. <br><br />
C) Angular momentum is equal to inertia times angular speed, and we establish below that angular velocity changes. <br><br />
D) Angular velocity changes since a constant force is being applied to the object, so it's speed/velocity must inherently increase. <br><br />
E) Because the torque being applied is constant, angular acceleration does not change (remember, acceleration is a measure of the rate of change of velocity!). <br><br />
<br />
===Middling===<br />
[[File:Screen Shot 2015-12-05 at 9.47.39 PM.png]]<br />
<br />
[[File:Solution.png]]<br />
<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
A general description of torque:<br />
http://www.physicsbook.gatech.edu/Torque<br />
<br />
===External links===<br />
A brief overview on the topic: [https://www.youtube.com/watch?v=mvzSjRFQbHE]<br />
<br />
==References==<br />
<br />
Matters and Interactions: 4th Edition <br><br />
WebAssign <br><br />
College Physics: Ninth Edition by Raymond Serway and Chris Vuille <br><br />
[[Category:Which Category did you place this in?]]</div>Nvohra3http://www.physicsbook.gatech.edu/index.php?title=File:Solution.jpg&diff=19159File:Solution.jpg2015-12-06T03:37:49Z<p>Nvohra3: Solution to non-zero torque question.</p>
<hr />
<div>Solution to non-zero torque question.</div>Nvohra3http://www.physicsbook.gatech.edu/index.php?title=Systems_with_Nonzero_Torque&diff=18685Systems with Nonzero Torque2015-12-06T02:56:14Z<p>Nvohra3: /* The Main Idea */</p>
<hr />
<div>Claimed by nvohra3.<br />
<br />
In certain systems, external torques have an effect on a system's angular momentum. Since these external forces do not sum to zero, we end up with a system with nonzero torque.<br />
<br />
==The Main Idea==<br />
<br />
With previous systems involving torque, we've been fortunate enough to have systems where the net torque is non-zero, hence <math> \vec{L}_{final} = \vec{L}_{initial}. </math> <br><br />
See systems with zero net torque in "See Also" section below for more information. <br><br />
<br />
However, we're not always fortunate enough to have such systems. In such cases, our computations become a little more complicated, and we'll see how below.<br />
<br />
===A Mathematical Model===<br />
<br />
So the angular momentum principle is the following: <math>{\frac{d\vec{L}}{dt}}= \vec{r} * \vec{F}_{net} = \vec{т}_{net} </math><br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Taken from sources listed at bottom of page.<br />
<br />
===Simple===<br />
A constant net nonzero torque is exerted on an object. Which of the following quantities cannot be constant for this object? <br><br />
A) Moment of inertia <br><br />
B) Center of mass <br><br />
C) Angular momentum <br><br />
D) Angular velocity <br><br />
E) Angular acceleration <br><br />
<br><br />
Solution/Explanation: <br><br />
C, D. Why? <br><br />
A) Moment of inertia does not change depending on whether torque is exerted on an object; moment of inertia depends on the object and axis of rotation, nothing more. <br><br />
B) Center of mass doesn't change with applied torque as well. <br><br />
C) Angular momentum is equal to inertia times angular speed, and we establish below that angular velocity changes. <br><br />
D) Angular velocity changes since a constant force is being applied to the object, so it's speed/velocity must inherently increase. <br><br />
E) Because the torque being applied is constant, angular acceleration does not change (remember, acceleration is a measure of the rate of change of velocity!). <br><br />
<br />
===Middling===<br />
[[File:Screen Shot 2015-12-05 at 9.47.39 PM.png]]<br />
<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
A general description of torque:<br />
http://www.physicsbook.gatech.edu/Torque<br />
<br />
===External links===<br />
A brief overview on the topic: [https://www.youtube.com/watch?v=mvzSjRFQbHE]<br />
<br />
==References==<br />
<br />
Matters and Interactions: 4th Edition <br><br />
WebAssign <br><br />
College Physics: Ninth Edition by Raymond Serway and Chris Vuille <br><br />
[[Category:Which Category did you place this in?]]</div>Nvohra3http://www.physicsbook.gatech.edu/index.php?title=Systems_with_Nonzero_Torque&diff=18615Systems with Nonzero Torque2015-12-06T02:49:26Z<p>Nvohra3: /* Middling */</p>
<hr />
<div>Claimed by nvohra3.<br />
<br />
In certain systems, external torques have an effect on a system's angular momentum. Since these external forces do not sum to zero, we end up with a system with nonzero torque.<br />
<br />
==The Main Idea==<br />
<br />
With previous systems involving torque, we've been fortunate enough to have systems where the net torque is non-zero, hence <math> \vec{L}_{final} = \vec{L}_{initial}. </math><br />
See <br />
However, we're not always fortunate enough to have such systems.<br />
<br />
===A Mathematical Model===<br />
<br />
So the angular momentum principle is the following: <math>{\frac{d\vec{L}}{dt}}= \vec{r} * \vec{F}_{net} = \vec{т}_{net} </math><br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Taken from sources listed at bottom of page.<br />
<br />
===Simple===<br />
A constant net nonzero torque is exerted on an object. Which of the following quantities cannot be constant for this object? <br><br />
A) Moment of inertia <br><br />
B) Center of mass <br><br />
C) Angular momentum <br><br />
D) Angular velocity <br><br />
E) Angular acceleration <br><br />
<br><br />
Solution/Explanation: <br><br />
C, D. Why? <br><br />
A) Moment of inertia does not change depending on whether torque is exerted on an object; moment of inertia depends on the object and axis of rotation, nothing more. <br><br />
B) Center of mass doesn't change with applied torque as well. <br><br />
C) Angular momentum is equal to inertia times angular speed, and we establish below that angular velocity changes. <br><br />
D) Angular velocity changes since a constant force is being applied to the object, so it's speed/velocity must inherently increase. <br><br />
E) Because the torque being applied is constant, angular acceleration does not change (remember, acceleration is a measure of the rate of change of velocity!). <br><br />
<br />
===Middling===<br />
[[File:Screen Shot 2015-12-05 at 9.47.39 PM.png]]<br />
<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
A general description of torque:<br />
http://www.physicsbook.gatech.edu/Torque<br />
<br />
===External links===<br />
A brief overview on the topic: [https://www.youtube.com/watch?v=mvzSjRFQbHE]<br />
<br />
==References==<br />
<br />
Matters and Interactions: 4th Edition <br><br />
WebAssign <br><br />
College Physics: Ninth Edition by Raymond Serway and Chris Vuille <br><br />
[[Category:Which Category did you place this in?]]</div>Nvohra3http://www.physicsbook.gatech.edu/index.php?title=File:Screen_Shot_2015-12-05_at_9.47.39_PM.png&diff=18607File:Screen Shot 2015-12-05 at 9.47.39 PM.png2015-12-06T02:48:31Z<p>Nvohra3: Nonzero Net Torque Book Example</p>
<hr />
<div>Nonzero Net Torque Book Example</div>Nvohra3http://www.physicsbook.gatech.edu/index.php?title=Systems_with_Nonzero_Torque&diff=18596Systems with Nonzero Torque2015-12-06T02:46:44Z<p>Nvohra3: /* Middling */</p>
<hr />
<div>Claimed by nvohra3.<br />
<br />
In certain systems, external torques have an effect on a system's angular momentum. Since these external forces do not sum to zero, we end up with a system with nonzero torque.<br />
<br />
==The Main Idea==<br />
<br />
With previous systems involving torque, we've been fortunate enough to have systems where the net torque is non-zero, hence <math> \vec{L}_{final} = \vec{L}_{initial}. </math><br />
See <br />
However, we're not always fortunate enough to have such systems.<br />
<br />
===A Mathematical Model===<br />
<br />
So the angular momentum principle is the following: <math>{\frac{d\vec{L}}{dt}}= \vec{r} * \vec{F}_{net} = \vec{т}_{net} </math><br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Taken from sources listed at bottom of page.<br />
<br />
===Simple===<br />
A constant net nonzero torque is exerted on an object. Which of the following quantities cannot be constant for this object? <br><br />
A) Moment of inertia <br><br />
B) Center of mass <br><br />
C) Angular momentum <br><br />
D) Angular velocity <br><br />
E) Angular acceleration <br><br />
<br><br />
Solution/Explanation: <br><br />
C, D. Why? <br><br />
A) Moment of inertia does not change depending on whether torque is exerted on an object; moment of inertia depends on the object and axis of rotation, nothing more. <br><br />
B) Center of mass doesn't change with applied torque as well. <br><br />
C) Angular momentum is equal to inertia times angular speed, and we establish below that angular velocity changes. <br><br />
D) Angular velocity changes since a constant force is being applied to the object, so it's speed/velocity must inherently increase. <br><br />
E) Because the torque being applied is constant, angular acceleration does not change (remember, acceleration is a measure of the rate of change of velocity!). <br><br />
<br />
===Middling===<br />
[[File:Example.jpg]]<br />
<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
A general description of torque:<br />
http://www.physicsbook.gatech.edu/Torque<br />
<br />
===External links===<br />
A brief overview on the topic: [https://www.youtube.com/watch?v=mvzSjRFQbHE]<br />
<br />
==References==<br />
<br />
Matters and Interactions: 4th Edition <br><br />
WebAssign <br><br />
College Physics: Ninth Edition by Raymond Serway and Chris Vuille <br><br />
[[Category:Which Category did you place this in?]]</div>Nvohra3http://www.physicsbook.gatech.edu/index.php?title=Systems_with_Nonzero_Torque&diff=18539Systems with Nonzero Torque2015-12-06T02:39:36Z<p>Nvohra3: /* Simple */</p>
<hr />
<div>Claimed by nvohra3.<br />
<br />
In certain systems, external torques have an effect on a system's angular momentum. Since these external forces do not sum to zero, we end up with a system with nonzero torque.<br />
<br />
==The Main Idea==<br />
<br />
With previous systems involving torque, we've been fortunate enough to have systems where the net torque is non-zero, hence <math> \vec{L}_{final} = \vec{L}_{initial}. </math><br />
See <br />
However, we're not always fortunate enough to have such systems.<br />
<br />
===A Mathematical Model===<br />
<br />
So the angular momentum principle is the following: <math>{\frac{d\vec{L}}{dt}}= \vec{r} * \vec{F}_{net} = \vec{т}_{net} </math><br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Taken from sources listed at bottom of page.<br />
<br />
===Simple===<br />
A constant net nonzero torque is exerted on an object. Which of the following quantities cannot be constant for this object? <br><br />
A) Moment of inertia <br><br />
B) Center of mass <br><br />
C) Angular momentum <br><br />
D) Angular velocity <br><br />
E) Angular acceleration <br><br />
<br><br />
Solution/Explanation: <br><br />
C, D. Why? <br><br />
A) Moment of inertia does not change depending on whether torque is exerted on an object; moment of inertia depends on the object and axis of rotation, nothing more. <br><br />
B) Center of mass doesn't change with applied torque as well. <br><br />
C) Angular momentum is equal to inertia times angular speed, and we establish below that angular velocity changes. <br><br />
D) Angular velocity changes since a constant force is being applied to the object, so it's speed/velocity must inherently increase. <br><br />
E) Because the torque being applied is constant, angular acceleration does not change (remember, acceleration is a measure of the rate of change of velocity!). <br><br />
<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
A general description of torque:<br />
http://www.physicsbook.gatech.edu/Torque<br />
<br />
===External links===<br />
A brief overview on the topic: [https://www.youtube.com/watch?v=mvzSjRFQbHE]<br />
<br />
==References==<br />
<br />
Matters and Interactions: 4th Edition <br><br />
WebAssign <br><br />
College Physics: Ninth Edition by Raymond Serway and Chris Vuille <br><br />
[[Category:Which Category did you place this in?]]</div>Nvohra3http://www.physicsbook.gatech.edu/index.php?title=Systems_with_Nonzero_Torque&diff=18531Systems with Nonzero Torque2015-12-06T02:38:53Z<p>Nvohra3: /* References */</p>
<hr />
<div>Claimed by nvohra3.<br />
<br />
In certain systems, external torques have an effect on a system's angular momentum. Since these external forces do not sum to zero, we end up with a system with nonzero torque.<br />
<br />
==The Main Idea==<br />
<br />
With previous systems involving torque, we've been fortunate enough to have systems where the net torque is non-zero, hence <math> \vec{L}_{final} = \vec{L}_{initial}. </math><br />
See <br />
However, we're not always fortunate enough to have such systems.<br />
<br />
===A Mathematical Model===<br />
<br />
So the angular momentum principle is the following: <math>{\frac{d\vec{L}}{dt}}= \vec{r} * \vec{F}_{net} = \vec{т}_{net} </math><br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Taken from sources listed at bottom of page.<br />
<br />
===Simple===<br />
A constant net nonzero torque is exerted on an object. Which of the following quantities cannot be constant for this object?<br />
A) Moment of inertia<br />
B) Center of mass<br />
C) Angular momentum<br />
D) Angular velocity<br />
E) Angular acceleration<br />
<br />
Solution/Explanation:<br />
C, D. Why?<br />
A) Moment of inertia does not change depending on whether torque is exerted on an object; moment of inertia depends on the object and axis of rotation, nothing more.<br />
B) Center of mass doesn't change with applied torque as well.<br />
C) Angular momentum is equal to inertia times angular speed, and we establish below that angular velocity changes.<br />
D) Angular velocity changes since a constant force is being applied to the object, causing the object to<br />
E) Because the torque being applied is constant, angular acceleration does not change (remember, acceleration is a measure of the rate of change of velocity!).<br />
<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
A general description of torque:<br />
http://www.physicsbook.gatech.edu/Torque<br />
<br />
===External links===<br />
A brief overview on the topic: [https://www.youtube.com/watch?v=mvzSjRFQbHE]<br />
<br />
==References==<br />
<br />
Matters and Interactions: 4th Edition <br><br />
WebAssign <br><br />
College Physics: Ninth Edition by Raymond Serway and Chris Vuille <br><br />
[[Category:Which Category did you place this in?]]</div>Nvohra3http://www.physicsbook.gatech.edu/index.php?title=Systems_with_Nonzero_Torque&diff=18523Systems with Nonzero Torque2015-12-06T02:38:12Z<p>Nvohra3: /* References */</p>
<hr />
<div>Claimed by nvohra3.<br />
<br />
In certain systems, external torques have an effect on a system's angular momentum. Since these external forces do not sum to zero, we end up with a system with nonzero torque.<br />
<br />
==The Main Idea==<br />
<br />
With previous systems involving torque, we've been fortunate enough to have systems where the net torque is non-zero, hence <math> \vec{L}_{final} = \vec{L}_{initial}. </math><br />
See <br />
However, we're not always fortunate enough to have such systems.<br />
<br />
===A Mathematical Model===<br />
<br />
So the angular momentum principle is the following: <math>{\frac{d\vec{L}}{dt}}= \vec{r} * \vec{F}_{net} = \vec{т}_{net} </math><br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Taken from sources listed at bottom of page.<br />
<br />
===Simple===<br />
A constant net nonzero torque is exerted on an object. Which of the following quantities cannot be constant for this object?<br />
A) Moment of inertia<br />
B) Center of mass<br />
C) Angular momentum<br />
D) Angular velocity<br />
E) Angular acceleration<br />
<br />
Solution/Explanation:<br />
C, D. Why?<br />
A) Moment of inertia does not change depending on whether torque is exerted on an object; moment of inertia depends on the object and axis of rotation, nothing more.<br />
B) Center of mass doesn't change with applied torque as well.<br />
C) Angular momentum is equal to inertia times angular speed, and we establish below that angular velocity changes.<br />
D) Angular velocity changes since a constant force is being applied to the object, causing the object to<br />
E) Because the torque being applied is constant, angular acceleration does not change (remember, acceleration is a measure of the rate of change of velocity!).<br />
<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
A general description of torque:<br />
http://www.physicsbook.gatech.edu/Torque<br />
<br />
===External links===<br />
A brief overview on the topic: [https://www.youtube.com/watch?v=mvzSjRFQbHE]<br />
<br />
==References==<br />
<br />
Matters and Interactions: 4th Edition<br />
WebAssign<br />
College Physics: Ninth Edition by Raymond Serway and Chris Vuille<br />
[[Category:Which Category did you place this in?]]</div>Nvohra3http://www.physicsbook.gatech.edu/index.php?title=Systems_with_Nonzero_Torque&diff=18515Systems with Nonzero Torque2015-12-06T02:37:37Z<p>Nvohra3: /* Examples */</p>
<hr />
<div>Claimed by nvohra3.<br />
<br />
In certain systems, external torques have an effect on a system's angular momentum. Since these external forces do not sum to zero, we end up with a system with nonzero torque.<br />
<br />
==The Main Idea==<br />
<br />
With previous systems involving torque, we've been fortunate enough to have systems where the net torque is non-zero, hence <math> \vec{L}_{final} = \vec{L}_{initial}. </math><br />
See <br />
However, we're not always fortunate enough to have such systems.<br />
<br />
===A Mathematical Model===<br />
<br />
So the angular momentum principle is the following: <math>{\frac{d\vec{L}}{dt}}= \vec{r} * \vec{F}_{net} = \vec{т}_{net} </math><br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Taken from sources listed at bottom of page.<br />
<br />
===Simple===<br />
A constant net nonzero torque is exerted on an object. Which of the following quantities cannot be constant for this object?<br />
A) Moment of inertia<br />
B) Center of mass<br />
C) Angular momentum<br />
D) Angular velocity<br />
E) Angular acceleration<br />
<br />
Solution/Explanation:<br />
C, D. Why?<br />
A) Moment of inertia does not change depending on whether torque is exerted on an object; moment of inertia depends on the object and axis of rotation, nothing more.<br />
B) Center of mass doesn't change with applied torque as well.<br />
C) Angular momentum is equal to inertia times angular speed, and we establish below that angular velocity changes.<br />
D) Angular velocity changes since a constant force is being applied to the object, causing the object to<br />
E) Because the torque being applied is constant, angular acceleration does not change (remember, acceleration is a measure of the rate of change of velocity!).<br />
<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
A general description of torque:<br />
http://www.physicsbook.gatech.edu/Torque<br />
<br />
===External links===<br />
A brief overview on the topic: [https://www.youtube.com/watch?v=mvzSjRFQbHE]<br />
<br />
==References==<br />
<br />
Matters and Interactions: 4th Edition<br />
<br />
[[Category:Which Category did you place this in?]]</div>Nvohra3http://www.physicsbook.gatech.edu/index.php?title=Systems_with_Nonzero_Torque&diff=18510Systems with Nonzero Torque2015-12-06T02:37:13Z<p>Nvohra3: /* Simple */</p>
<hr />
<div>Claimed by nvohra3.<br />
<br />
In certain systems, external torques have an effect on a system's angular momentum. Since these external forces do not sum to zero, we end up with a system with nonzero torque.<br />
<br />
==The Main Idea==<br />
<br />
With previous systems involving torque, we've been fortunate enough to have systems where the net torque is non-zero, hence <math> \vec{L}_{final} = \vec{L}_{initial}. </math><br />
See <br />
However, we're not always fortunate enough to have such systems.<br />
<br />
===A Mathematical Model===<br />
<br />
So the angular momentum principle is the following: <math>{\frac{d\vec{L}}{dt}}= \vec{r} * \vec{F}_{net} = \vec{т}_{net} </math><br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Taken from WebAssign and/or Matters and Interactions: Fourth Edition<br />
<br />
===Simple===<br />
A constant net nonzero torque is exerted on an object. Which of the following quantities cannot be constant for this object?<br />
A) Moment of inertia<br />
B) Center of mass<br />
C) Angular momentum<br />
D) Angular velocity<br />
E) Angular acceleration<br />
<br />
Solution/Explanation:<br />
C, D. Why?<br />
A) Moment of inertia does not change depending on whether torque is exerted on an object; moment of inertia depends on the object and axis of rotation, nothing more.<br />
B) Center of mass doesn't change with applied torque as well.<br />
C) Angular momentum is equal to inertia times angular speed, and we establish below that angular velocity changes.<br />
D) Angular velocity changes since a constant force is being applied to the object, causing the object to<br />
E) Because the torque being applied is constant, angular acceleration does not change (remember, acceleration is a measure of the rate of change of velocity!).<br />
<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
A general description of torque:<br />
http://www.physicsbook.gatech.edu/Torque<br />
<br />
===External links===<br />
A brief overview on the topic: [https://www.youtube.com/watch?v=mvzSjRFQbHE]<br />
<br />
==References==<br />
<br />
Matters and Interactions: 4th Edition<br />
<br />
[[Category:Which Category did you place this in?]]</div>Nvohra3http://www.physicsbook.gatech.edu/index.php?title=Systems_with_Nonzero_Torque&diff=18380Systems with Nonzero Torque2015-12-06T02:20:06Z<p>Nvohra3: /* Examples */</p>
<hr />
<div>Claimed by nvohra3.<br />
<br />
In certain systems, external torques have an effect on a system's angular momentum. Since these external forces do not sum to zero, we end up with a system with nonzero torque.<br />
<br />
==The Main Idea==<br />
<br />
With previous systems involving torque, we've been fortunate enough to have systems where the net torque is non-zero, hence <math> \vec{L}_{final} = \vec{L}_{initial}. </math><br />
See <br />
However, we're not always fortunate enough to have such systems.<br />
<br />
===A Mathematical Model===<br />
<br />
So the angular momentum principle is the following: <math>{\frac{d\vec{L}}{dt}}= \vec{r} * \vec{F}_{net} = \vec{т}_{net} </math><br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Taken from WebAssign and/or Matters and Interactions: Fourth Edition<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
A general description of torque:<br />
http://www.physicsbook.gatech.edu/Torque<br />
<br />
===External links===<br />
A brief overview on the topic: [https://www.youtube.com/watch?v=mvzSjRFQbHE]<br />
<br />
==References==<br />
<br />
Matters and Interactions: 4th Edition<br />
<br />
[[Category:Which Category did you place this in?]]</div>Nvohra3http://www.physicsbook.gatech.edu/index.php?title=Systems_with_Nonzero_Torque&diff=18147Systems with Nonzero Torque2015-12-06T01:51:08Z<p>Nvohra3: /* The Main Idea */</p>
<hr />
<div>Claimed by nvohra3.<br />
<br />
In certain systems, external torques have an effect on a system's angular momentum. Since these external forces do not sum to zero, we end up with a system with nonzero torque.<br />
<br />
==The Main Idea==<br />
<br />
With previous systems involving torque, we've been fortunate enough to have systems where the net torque is non-zero, hence <math> \vec{L}_{final} = \vec{L}_{initial}. </math><br />
See <br />
However, we're not always fortunate enough to have such systems.<br />
<br />
===A Mathematical Model===<br />
<br />
So the angular momentum principle is the following: <math>{\frac{d\vec{L}}{dt}}= \vec{r} * \vec{F}_{net} = \vec{т}_{net} </math><br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
A general description of torque:<br />
http://www.physicsbook.gatech.edu/Torque<br />
<br />
===External links===<br />
A brief overview on the topic: [https://www.youtube.com/watch?v=mvzSjRFQbHE]<br />
<br />
==References==<br />
<br />
Matters and Interactions: 4th Edition<br />
<br />
[[Category:Which Category did you place this in?]]</div>Nvohra3http://www.physicsbook.gatech.edu/index.php?title=Systems_with_Nonzero_Torque&diff=18021Systems with Nonzero Torque2015-12-06T01:39:40Z<p>Nvohra3: /* References */</p>
<hr />
<div>Claimed by nvohra3.<br />
<br />
In certain systems, external torques have an effect on a system's angular momentum. Since these external forces do not sum to zero, we end up with a system with nonzero torque.<br />
<br />
==The Main Idea==<br />
<br />
We can relate this to the Angular Momentum principle <math>{\frac{d\vec{L}}{dt}}=Torque</math><br />
<br />
===A Mathematical Model===<br />
<br />
What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.<br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
A general description of torque:<br />
http://www.physicsbook.gatech.edu/Torque<br />
<br />
===External links===<br />
A brief overview on the topic: [https://www.youtube.com/watch?v=mvzSjRFQbHE]<br />
<br />
==References==<br />
<br />
Matters and Interactions: 4th Edition<br />
<br />
[[Category:Which Category did you place this in?]]</div>Nvohra3http://www.physicsbook.gatech.edu/index.php?title=Systems_with_Nonzero_Torque&diff=17996Systems with Nonzero Torque2015-12-06T01:36:18Z<p>Nvohra3: /* External links */</p>
<hr />
<div>Claimed by nvohra3.<br />
<br />
In certain systems, external torques have an effect on a system's angular momentum. Since these external forces do not sum to zero, we end up with a system with nonzero torque.<br />
<br />
==The Main Idea==<br />
<br />
We can relate this to the Angular Momentum principle <math>{\frac{d\vec{L}}{dt}}=Torque</math><br />
<br />
===A Mathematical Model===<br />
<br />
What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.<br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
A general description of torque:<br />
http://www.physicsbook.gatech.edu/Torque<br />
<br />
===External links===<br />
A brief overview on the topic: [https://www.youtube.com/watch?v=mvzSjRFQbHE]<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Nvohra3http://www.physicsbook.gatech.edu/index.php?title=Systems_with_Nonzero_Torque&diff=17991Systems with Nonzero Torque2015-12-06T01:35:58Z<p>Nvohra3: /* External links */</p>
<hr />
<div>Claimed by nvohra3.<br />
<br />
In certain systems, external torques have an effect on a system's angular momentum. Since these external forces do not sum to zero, we end up with a system with nonzero torque.<br />
<br />
==The Main Idea==<br />
<br />
We can relate this to the Angular Momentum principle <math>{\frac{d\vec{L}}{dt}}=Torque</math><br />
<br />
===A Mathematical Model===<br />
<br />
What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.<br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
A general description of torque:<br />
http://www.physicsbook.gatech.edu/Torque<br />
<br />
===External links===<br />
[https://www.youtube.com/watch?v=mvzSjRFQbHE]<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Nvohra3http://www.physicsbook.gatech.edu/index.php?title=Systems_with_Nonzero_Torque&diff=17978Systems with Nonzero Torque2015-12-06T01:34:09Z<p>Nvohra3: /* Further reading */</p>
<hr />
<div>Claimed by nvohra3.<br />
<br />
In certain systems, external torques have an effect on a system's angular momentum. Since these external forces do not sum to zero, we end up with a system with nonzero torque.<br />
<br />
==The Main Idea==<br />
<br />
We can relate this to the Angular Momentum principle <math>{\frac{d\vec{L}}{dt}}=Torque</math><br />
<br />
===A Mathematical Model===<br />
<br />
What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.<br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
A general description of torque:<br />
http://www.physicsbook.gatech.edu/Torque<br />
<br />
===External links===<br />
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Nvohra3http://www.physicsbook.gatech.edu/index.php?title=Systems_with_Nonzero_Torque&diff=17848Systems with Nonzero Torque2015-12-06T01:17:15Z<p>Nvohra3: /* See also */</p>
<hr />
<div>Claimed by nvohra3.<br />
<br />
In certain systems, external torques have an effect on a system's angular momentum. Since these external forces do not sum to zero, we end up with a system with nonzero torque.<br />
<br />
==The Main Idea==<br />
<br />
We can relate this to the Angular Momentum principle <math>{\frac{d\vec{L}}{dt}}=Torque</math><br />
<br />
===A Mathematical Model===<br />
<br />
What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.<br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
A general description of torque:<br />
http://www.physicsbook.gatech.edu/Torque<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Nvohra3http://www.physicsbook.gatech.edu/index.php?title=Systems_with_Nonzero_Torque&diff=15164Systems with Nonzero Torque2015-12-05T20:18:20Z<p>Nvohra3: </p>
<hr />
<div>Claimed by nvohra3.<br />
<br />
In certain systems, external torques have an effect on a system's angular momentum. Since these external forces do not sum to zero, we end up with a system with nonzero torque.<br />
<br />
==The Main Idea==<br />
<br />
We can relate this to the Angular Momentum principle <math>{\frac{d\vec{L}}{dt}}=Torque</math><br />
<br />
===A Mathematical Model===<br />
<br />
What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.<br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]<br />
<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Nvohra3