Friction

2016-11-27T19:34:20Z

Drao31: /* A Mathematical Model */

Friction

2016-11-27T19:33:42Z

Drao31: /* The Main Idea */

Rotational Kinematics

2016-11-27T07:57:29Z

Drao31:

==The Main Idea==

Rotational motion is defined as an object moving around an axis in contrast to translational motion which involves the object moving in a straight trajectory.

===A Mathematical Model===

Rotation can be characterized by its angular velocity and angular acceleration. The equations are listed below.

Angular velocity:

:<math>\boldsymbol{{w}} = \frac{\boldsymbol{v}}{\boldsymbol{r}}</math> ,
where <math>{\boldsymbol{v}}</math> is the velocity of the object and <math>{\boldsymbol{r}}</math> is the radius of the circle of motion. It can also be represented as the change in angle over the distance traveled in the formula shown below:

:<math>\boldsymbol{{w}} = \frac{\boldsymbol{d\theta}}{\boldsymbol{dt}}</math> , where <math>{\boldsymbol{d\theta}}</math> is the change in angle and <math>{\boldsymbol{dt}}</math> is the change in time.

[[File:angularvelocity.png]]

Angular velocity always has a unit of radians (radians/sec or radians/hr).

Angular acceleration is equal to alpha:

:<math>\boldsymbol{{\alpha}} = \frac{\boldsymbol{a_t}}{\boldsymbol{r}}</math> ,
where <math>{\boldsymbol{a_t}}</math> is the tangential acceleration of the object and <math>{\boldsymbol{r}}</math> is the radius of the circle of motion.

Rotational Kinetic Energy:
An object with a center of mass at rest can still have rotational kinetic energy. For example, if a disk is suspended in the air and spun, it has no translational kinetic energy. The position of the disk does not change. However, since it is spinning (rotating), it still has kinetic energy. To account for this, we can relate angular velocity with the moment of inertia of the object to find a value for the rotational kinetic energy.

Rotational Kinetic Energy:

::<math>{KE}_{rot} = \frac{{1}}{{2}}{I}_{cm}{ω^2}</math>

Relation to Work and Energy Principle:

The energy principle states:
::<math>{E}_{f} = {E}_{i} + W </math>

We can apply the energy principle to rotational kinetic energy as well to find changes in kinetic energy and work done on the system.

===A Computational Model===

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===

A simple example and application of the concept of rotation is the earth's rotation on it's axis. It rotates once every 24 hours. What is the angular velocity?

:<math>\boldsymbol{{w}} = \frac{\boldsymbol{d\theta}}{\boldsymbol{dt}}</math>
:<math>\boldsymbol{{w}} = \frac{\boldsymbol{2\pi}}{\boldsymbol{24}}</math>
:<math>\boldsymbol{{w}} = \frac{\boldsymbol{\pi}}{\boldsymbol{12}}</math>
:<math>\boldsymbol{{w}} = \frac{\boldsymbol{\pi}}{\boldsymbol{12}}*\frac{\boldsymbol{180}}{\boldsymbol{\pi}}</math>
:<math>\boldsymbol{{w}} = {\boldsymbol{15 degrees}}</math>

Angular velocity can also be represented as change in angle (theta) over change in time. In this case, the earth rotates 2pi radians in 24 hours which reduces to pi/12 radians and that becomes 15 degrees.

===Middling===

A cylinder with a 2.5 ft radius is rotating at 120 rpm. Find the angular velocity in rad/sec and in degrees/sec. Find the linear velocity of a point on its rim in mph.

To find the solution of this problem, rpm (revolutions per minute) should be converted to radians/second. Following this, the linear velocity can be calculated by using the v=wr formula shown above. The angular velocity is 720 degrees per sec and the linear velocity is 21.42 mph.

Details of Explanation:

[[File:MiddlePrb.jpg]]

===Difficult===

A tire with a 9 inch radius is rotating at 30 mph. Find the angular velocity at a point on its rim. Also express the result in revolutions per minute.

[[File:Difficultprb.jpg]]

==Connectedness==
Rotation is an extremely important aspect of dynamics (the study of moving objects) which plays a big role in biomechanics. Rotation relates to several important body parts such as the shoulder where there are two axis of rotation, the medial-lateral axis and the anterior-posterior axis. A study of the movement of the shoulder helps to treat medical conditions that may affect this area. Dynamics is also very important in many other disciples, including mechanical engineering and aerospace engineering.

== See also ==

To learn more about Rotation in a more complete context, please refer to Torque or Rigid-Body Objects or Angular Momentum.

===Further reading===

Books, Articles or other print media on this topic

===External links===

Some other resources to further understand rotation are the following:

http://www.mathwarehouse.com/transformations/rotations-in-math.php

http://demonstrations.wolfram.com/Understanding3DRotation/

==References==

[1] Biomechanics, Basic. “It Is Important When Learning about (n.d.): n. pag. Web.

[2] "Angular Velocity and Angular Acceleration." Van Nostrand's Scientific Encyclopedia (2005): n. pag. Web

Friction

2016-11-27T05:29:38Z

Drao31: /* A Computational Model */

Friction

2016-11-27T05:26:14Z

Drao31: /* A Computational Model */

File:Friction.gif

2016-11-27T05:24:07Z

2016-11-27T02:32:49Z

Drao31:

This page discusses the concept of friction and how it relates to both moving and static objects.

Claimed by drao31

==The Main Idea==

===A Mathematical Model===

===A Computational Model===

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]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
===Middling===
===Difficult===

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Contact Forces]]

Rotational Kinematics

2016-11-27T02:28:02Z

Drao31:

drao31
==The Main Idea==

Rotational motion is defined as an object moving around an axis in contrast to translational motion which involves the object moving in a straight trajectory.

===A Mathematical Model===

Rotation can be characterized by its angular velocity and angular acceleration. The equations are listed below.

Angular velocity:

:<math>\boldsymbol{{w}} = \frac{\boldsymbol{v}}{\boldsymbol{r}}</math> ,
where <math>{\boldsymbol{v}}</math> is the velocity of the object and <math>{\boldsymbol{r}}</math> is the radius of the circle of motion. It can also be represented as the change in angle over the distance traveled in the formula shown below:

:<math>\boldsymbol{{w}} = \frac{\boldsymbol{d\theta}}{\boldsymbol{dt}}</math> , where <math>{\boldsymbol{d\theta}}</math> is the change in angle and <math>{\boldsymbol{dt}}</math> is the change in time.

[[File:angularvelocity.png]]

Angular velocity always has a unit of radians (radians/sec or radians/hr).

Angular acceleration is equal to alpha:

:<math>\boldsymbol{{\alpha}} = \frac{\boldsymbol{a_t}}{\boldsymbol{r}}</math> ,
where <math>{\boldsymbol{a_t}}</math> is the tangential acceleration of the object and <math>{\boldsymbol{r}}</math> is the radius of the circle of motion.

Rotational Kinetic Energy:
An object with a center of mass at rest can still have rotational kinetic energy. For example, if a disk is suspended in the air and spun, it has no translational kinetic energy. The position of the disk does not change. However, since it is spinning (rotating), it still has kinetic energy. To account for this, we can relate angular velocity with the moment of inertia of the object to find a value for the rotational kinetic energy.

Rotational Kinetic Energy:

::<math>{KE}_{rot} = \frac{{1}}{{2}}{I}_{cm}{ω^2}</math>

Relation to Work and Energy Principle:

The energy principle states:
::<math>{E}_{f} = {E}_{i} + W </math>

We can apply the energy principle to rotational kinetic energy as well to find changes in kinetic energy and work done on the system.

===A Computational Model===

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===

A simple example and application of the concept of rotation is the earth's rotation on it's axis. It rotates once every 24 hours. What is the angular velocity?

:<math>\boldsymbol{{w}} = \frac{\boldsymbol{d\theta}}{\boldsymbol{dt}}</math>
:<math>\boldsymbol{{w}} = \frac{\boldsymbol{2\pi}}{\boldsymbol{24}}</math>
:<math>\boldsymbol{{w}} = \frac{\boldsymbol{\pi}}{\boldsymbol{12}}</math>
:<math>\boldsymbol{{w}} = \frac{\boldsymbol{\pi}}{\boldsymbol{12}}*\frac{\boldsymbol{180}}{\boldsymbol{\pi}}</math>
:<math>\boldsymbol{{w}} = {\boldsymbol{15 degrees}}</math>

Angular velocity can also be represented as change in angle (theta) over change in time. In this case, the earth rotates 2pi radians in 24 hours which reduces to pi/12 radians and that becomes 15 degrees.

===Middling===

A cylinder with a 2.5 ft radius is rotating at 120 rpm. Find the angular velocity in rad/sec and in degrees/sec. Find the linear velocity of a point on its rim in mph.

To find the solution of this problem, rpm (revolutions per minute) should be converted to radians/second. Following this, the linear velocity can be calculated by using the v=wr formula shown above. The angular velocity is 720 degrees per sec and the linear velocity is 21.42 mph.

Details of Explanation:

[[File:MiddlePrb.jpg]]

===Difficult===

A tire with a 9 inch radius is rotating at 30 mph. Find the angular velocity at a point on its rim. Also express the result in revolutions per minute.

[[File:Difficultprb.jpg]]

==Connectedness==
Rotation is an extremely important aspect of dynamics (the study of moving objects) which plays a big role in biomechanics. Rotation relates to several important body parts such as the shoulder where there are two axis of rotation, the medial-lateral axis and the anterior-posterior axis. A study of the movement of the shoulder helps to treat medical conditions that may affect this area. Dynamics is also very important in many other disciples, including mechanical engineering and aerospace engineering.

== See also ==

To learn more about Rotation in a more complete context, please refer to Torque or Rigid-Body Objects or Angular Momentum.

===Further reading===

Books, Articles or other print media on this topic

===External links===

Some other resources to further understand rotation are the following:

http://www.mathwarehouse.com/transformations/rotations-in-math.php

http://demonstrations.wolfram.com/Understanding3DRotation/

==References==

[1] Biomechanics, Basic. “It Is Important When Learning about (n.d.): n. pag. Web.

[2] "Angular Velocity and Angular Acceleration." Van Nostrand's Scientific Encyclopedia (2005): n. pag. Web

2016-10-31T20:14:39Z

Drao31:

Claimed by drao31 10/2016

This page is all about rotation and it's relation to torque. This page is very much a work still in progress by sthevuthasan3.

==The Main Idea==

Rotational motion is defined as when an object moves about an axis in a circle versus translational motion which involves the object moving in a straight trajectory.

===A Mathematical Model===

Rotation can be characterized by its angular velocity and angular acceleration. The equations are listed below.

Angular velocity:

:<math>\boldsymbol{{w}} = \frac{\boldsymbol{v}}{\boldsymbol{r}}</math> ,
where <math>{\boldsymbol{v}}</math> is the velocity of the object and <math>{\boldsymbol{r}}</math> is the radius of the circle of motion. It can also be represented as the change in angle over the distance traveled in the formula shown below:

:<math>\boldsymbol{{w}} = \frac{\boldsymbol{d\theta}}{\boldsymbol{dt}}</math> , where <math>{\boldsymbol{d\theta}}</math> is the change in angle and <math>{\boldsymbol{dt}}</math> is the change in time.

[[File:angularvelocity.png]]

Angular velocity always has a unit of radians (radians/sec or radians/hr).

Angular acceleration is equal to alpha:

:<math>\boldsymbol{{\alpha}} = \frac{\boldsymbol{a_t}}{\boldsymbol{r}}</math> ,
where <math>{\boldsymbol{a_t}}</math> is the tangential acceleration of the object and <math>{\boldsymbol{r}}</math> is the radius of the circle of motion.

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===

A simple example and application of the concept of rotation is the earth's rotation on it's axis. It rotates once every 24 hours. What is the angular velocity?

:<math>\boldsymbol{{w}} = \frac{\boldsymbol{d\theta}}{\boldsymbol{dt}}</math>
:<math>\boldsymbol{{w}} = \frac{\boldsymbol{2\pi}}{\boldsymbol{24}}</math>
:<math>\boldsymbol{{w}} = \frac{\boldsymbol{\pi}}{\boldsymbol{12}}</math>
:<math>\boldsymbol{{w}} = \frac{\boldsymbol{\pi}}{\boldsymbol{12}}*\frac{\boldsymbol{180}}{\boldsymbol{\pi}}</math>
:<math>\boldsymbol{{w}} = {\boldsymbol{15 degrees}}</math>

Angular velocity can also be represented as change in angle (theta) over change in time. In this case, the earth rotates 2pi radians in 24 hours which reduces to pi/12 radians and that becomes 15 degrees.

===Middling===

A cylinder with a 2.5 ft radius is rotating at 120 rpm. Find the angular velocity in rad/sec and in degrees/sec. Find the linear velocity of a point on its rim in mph.

To find the solution of this problem, rpm (revolutions per minute) should be converted to radians/second. Following this, the linear velocity can be calculated by using the v=wr formula shown above. The angular velocity is 720 degrees per sec and the linear velocity is 21.42 mph.

Details of Explanation:

[[File:MiddlePrb.jpg]]

===Difficult===

A tire with a 9 inch radius is rotating at 30 mph. Find the angular velocity at a point on its rim. Also express the result in revolutions per minute.

[[File:Difficultprb.jpg]]

==Connectedness==
Rotation is an extremely important aspect of dynamics (the study of moving objects) which plays a big role in biomechanics. Rotation relates to several important body parts such as the shoulder where there are two axis of rotation, the medial-lateral axis and the anterior-posterior axis. A study of the movement of the shoulder helps to treat medical conditions that may affect this area. Dynamics is also very important in many other disciples, including mechanical engineering and aerospace engineering.

== See also ==

To learn more about Rotation in a more complete context, please refer to Torque or Rigid-Body Objects or Angular Momentum.

===Further reading===

Books, Articles or other print media on this topic

===External links===

Some other resources to further understand rotation are the following:

http://www.mathwarehouse.com/transformations/rotations-in-math.php

http://demonstrations.wolfram.com/Understanding3DRotation/

==References==

[1] Biomechanics, Basic. “It Is Important When Learning about (n.d.): n. pag. Web.

[2] "Angular Velocity and Angular Acceleration." Van Nostrand's Scientific Encyclopedia (2005): n. pag. Web