Systems with Nonzero Torque - Revision history

Jorge R at 08:40, 28 April 2026

2026-04-28T08:40:38Z

← Older revision		Revision as of 04:40, 28 April 2026
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	Gravitational Torque can also result from the mass of other object resting on the system. For example, imagine a bird resting on a perfectly horizontal tree branch, the weight of the bird creates a gravitational force <math>\vec{F}_g = m\vec{g}</math> on the branch. Assuming the branch is attached at one end to a tree, then this attachment point acts as a pivot, and the weight of the bird produces a torque about that pivot. Even though the bird is external to the branch, its mass contributes to the net gravitational torque on the system.		Gravitational Torque can also result from the mass of other object resting on the system. For example, imagine a bird resting on a perfectly horizontal tree branch, the weight of the bird creates a gravitational force <math>\vec{F}_g = m\vec{g}</math> on the branch. Assuming the branch is attached at one end to a tree, then this attachment point acts as a pivot, and the weight of the bird produces a torque about that pivot. Even though the bird is external to the branch, its mass contributes to the net gravitational torque on the system.

			[[File:Screenshot_2026-04-28_at_4.38.14_AM.png]]

	Gravitational toque tends to rotate a system downward until the center of mass aligns vertically with the pivot point. At that point the line connecting the pivot and the center of mass become parallel to the direction of the gravitational force (usually downward along the vertical axis).		Gravitational toque tends to rotate a system downward until the center of mass aligns vertically with the pivot point. At that point the line connecting the pivot and the center of mass become parallel to the direction of the gravitational force (usually downward along the vertical axis).

Jorge R: /* Gravitational Torque */

2026-04-28T08:12:59Z

Gravitational Torque

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	===Gravitational Torque===		===Gravitational Torque===

	A common and important source of toque in a system is the result of the force of gravity on a object. When the center of mass of an object does not lie on the axis of rotation, then the systems own mass introduces gravitational torque. The rotational affect of gravity can be modeled as the force <math>\vec{F}_g = m\vec{g}</math> acting on the object's center of gravity. When inserted into the formula for toque the affect of gravity looks like: <math>\vec{\tau}_g = \vec{r}_{CM} \times \vec{F}_g</math>, where \vec{F}_g is the force of gravity and \vec{r}_{CM} is the vector that points from the pivot point to the center of mass.		A common and important source of toque in a system is the result of the force of gravity on a object. When the center of mass of an object does not lie on the axis of rotation, then the systems own mass introduces gravitational torque. The rotational affect of gravity can be modeled as the force <math>\vec{F}_g = m\vec{g}</math> acting on the object's center of gravity. When inserted into the formula for toque the affect of gravity looks like: <math>\vec{\tau}_g = \vec{r}_{CM} \times \vec{F}_g</math>, where <math>\vec{F}_g</math> is the force of gravity and <math>\vec{r}_{CM}</math> is the vector that points from the pivot point to the center of mass.

	Gravitational Torque can also result from the mass of other object resting on the system. For example, imagine a bird resting on a perfectly horizontal tree branch, the weight of the bird creates a gravitational force <math>\vec{F}_g = m\vec{g}</math> on the branch. Assuming the branch is attached at one end to a tree, then this attachment point acts as a pivot, and the weight of the bird produces a torque about that pivot. Even though the bird is external to the branch, its mass contributes to the net gravitational torque on the system.		Gravitational Torque can also result from the mass of other object resting on the system. For example, imagine a bird resting on a perfectly horizontal tree branch, the weight of the bird creates a gravitational force <math>\vec{F}_g = m\vec{g}</math> on the branch. Assuming the branch is attached at one end to a tree, then this attachment point acts as a pivot, and the weight of the bird produces a torque about that pivot. Even though the bird is external to the branch, its mass contributes to the net gravitational torque on the system.

Jorge R at 08:10, 28 April 2026

2026-04-28T08:10:57Z

← Older revision		Revision as of 04:10, 28 April 2026
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	wheel.rotate(angle=dtheta, axis = axisOfRotation, origin = wheel.pos)		wheel.rotate(angle=dtheta, axis = axisOfRotation, origin = wheel.pos)
	t += delta_t		t += delta_t

			===Gravitational Torque===

			A common and important source of toque in a system is the result of the force of gravity on a object. When the center of mass of an object does not lie on the axis of rotation, then the systems own mass introduces gravitational torque. The rotational affect of gravity can be modeled as the force <math>\vec{F}_g = m\vec{g}</math> acting on the object's center of gravity. When inserted into the formula for toque the affect of gravity looks like: <math>\vec{\tau}_g = \vec{r}_{CM} \times \vec{F}_g</math>, where \vec{F}_g is the force of gravity and \vec{r}_{CM} is the vector that points from the pivot point to the center of mass.

			Gravitational Torque can also result from the mass of other object resting on the system. For example, imagine a bird resting on a perfectly horizontal tree branch, the weight of the bird creates a gravitational force <math>\vec{F}_g = m\vec{g}</math> on the branch. Assuming the branch is attached at one end to a tree, then this attachment point acts as a pivot, and the weight of the bird produces a torque about that pivot. Even though the bird is external to the branch, its mass contributes to the net gravitational torque on the system.

			Gravitational toque tends to rotate a system downward until the center of mass aligns vertically with the pivot point. At that point the line connecting the pivot and the center of mass become parallel to the direction of the gravitational force (usually downward along the vertical axis).

	==Examples==		==Examples==

Jorge R at 06:56, 28 April 2026

2026-04-28T06:56:51Z

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	''Edited by ~~Conner Rudzinski Fall 2018~~''		''Edited by Jorge Ramirez Spring 2026''

	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.		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.

Bbreer6: /* Non-Zero Torque System using magnitude of vectors and Given Angle */

2019-07-25T05:17:14Z

Non-Zero Torque System using magnitude of vectors and Given Angle

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	We will use the formula <math> \vec{т}_{net} = \vec{r} * \vec{F}_{net} * sin(theta)</math>		We will use the formula <math> \vec{т}_{net} = \vec{r} * \vec{F}_{net} * sin(theta)</math>
	This calculation becomes 57sin(30) and equals 17.5 Nm.		This calculation becomes 57sin(30) and equals 17.5 Nm.

			It is important to recognize that the computation involves a cross product, meaning it is not simply the multiplication of the magnitudes of the two vectors but rather the multiplication of the magnitudes of the two vectors AND the sine of the angle between them. The angle between the two vectors tells us information about how significant the lever arm is in terms of amplifying or decreasing the effect of a force, i.e., leverage.

	===Middling===		===Middling===

Bbreer6: /* How to Model in VPython */

2019-07-15T02:51:43Z

How to Model in VPython

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	===How to Model in VPython===		===How to Model in VPython===
	The following code should be self explanatory and can be used as a template for modeling a system involving torque.		The following code should be self explanatory and can be used as a template for modeling a system involving torque.
	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.		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. One could write their own sub-routine for the cross product and/or rotation, but since vPython comes with these routines, it is advantageous to exploit them.
	# -- coding: utf-8 --		# -- coding: utf-8 --
	from __future__ import division		from __future__ import division

Carudz at 17:17, 25 November 2018

2018-11-25T17:17:46Z

← Older revision		Revision as of 13:17, 25 November 2018
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	'''Edited by Conner Rudzinski''		''Edited by Conner Rudzinski Fall 2018''

	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.		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.

Carudz at 17:16, 25 November 2018

2018-11-25T17:16:29Z

← Older revision		Revision as of 13:16, 25 November 2018
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	'''~~Claimed~~ by ~~Emma Bivings~~''		'''Edited by Conner Rudzinski''

	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.		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.
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	==The Main Idea==		==The Main Idea==

	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>		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 systems with zero net torque in "See Also" section below for more information. <br>		See systems with zero net torque in "See Also" section below for more information. <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.		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.
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	The angular momentum principle is the following: <math>{\frac{d\vec{L}}{dt}}= \vec{r} * \vec{F}_{net} = \vec{т}_{net} </math> <br>		The angular momentum principle is the following: <math>{\frac{d\vec{L}}{dt}}= \vec{r} * \vec{F}_{net} = \vec{т}_{net} </math> <br>
	~~As previously mentioned, we~~'ll now look at the case where <math> \vec{F}_{net} </math> is NOT equal to 0.		This means that the calculation of torque is the cross product of the force and distance vectors. We'll now look at the case where <math> \vec{F}_{net} </math> is NOT equal to 0.

	===How to Model in VPython===		===How to Model in VPython===
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	D) Angular velocity changes since a constant force is being applied to the object, so it's speed/velocity must inherently increase. <br>		D) Angular velocity changes since a constant force is being applied to the object, so it's speed/velocity must inherently increase. <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>		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>

			===System with Non-Zero Torque Calculation===

			''Calculate the torque of a system with a distance vector <2,1,3> and a force vector of <4,3,5>.'' <br>
			This is a system with non-zero torque, so we will use the formula <math> \vec{т}_{net} = \vec{r} * \vec{F}_{net}</math>
			The cross product of <math>\vec{r} * \vec{F}_{net} </math> is <math>\vec{2,1,3} * \vec{4,3,5} </math>, creating the vector <math> \vec{-4,2,2} </math>. This is the torque vector.

			=== Non-Zero Torque System using magnitude of vectors and Given Angle===
			''Calculate the torque of a system with a distance magnitude of 5 meters and a force magnitude of 7 newtons, working at an angle of 30 degrees.'' <br>
			We will use the formula <math> \vec{т}_{net} = \vec{r} * \vec{F}_{net} * sin(theta)</math>
			This calculation becomes 57sin(30) and equals 17.5 Nm.

	===Middling===		===Middling===
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	==History==		==History==

			Torque is a calculation of the rotational force applied to the system.
	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.		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.

Ebivings3 at 01:26, 27 November 2016

2016-11-27T01:26:47Z

← Older revision		Revision as of 21:26, 26 November 2016
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			'''Claimed by Emma Bivings''

	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.		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.

Nvohra3: /* References */

2015-12-08T04:15:46Z

References

← Older revision		Revision as of 00:15, 8 December 2015
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	Matters and Interactions: 4th Edition <br>		Matters and Interactions: 4th Edition <br>
	~~WebAssign <br>~~		[https://drive.google.com/file/d/0B6hjEAwn8lB-WURaNmRvVGFjUnM/edit College Physics: Ninth Edition] <br>
	[ https://drive.google.com/file/d/0B6hjEAwn8lB-WURaNmRvVGFjUnM/edit College Physics: Ninth Edition] <br>
	[[Category:Angular Momentum]]		[[Category:Angular Momentum]]