Rotational Kinematics

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]\displaystyle{ \boldsymbol{{w}} = \frac{\boldsymbol{v}}{\boldsymbol{r}} }[/math] ,

where [math]\displaystyle{ {\boldsymbol{v}} }[/math] is the velocity of the object and [math]\displaystyle{ {\boldsymbol{r}} }[/math] is the radius of the circle of motion.

Angular acceleration is equal to alpha:

[math]\displaystyle{ \boldsymbol{{alpha}} = \frac{\boldsymbol{a_t}}{\boldsymbol{r}} }[/math] ,

where [math]\displaystyle{ {\boldsymbol{a_t}} }[/math] is the tangential acceleration of the object and [math]\displaystyle{ {\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]\displaystyle{ \boldsymbol{{w}} = \frac{\boldsymbol{theta}}{\boldsymbol{t}} }[/math]

[math]\displaystyle{ \boldsymbol{{w}} = \frac{\boldsymbol{2pi}}{\boldsymbol{24}} }[/math]

<math>\boldsymbolTemplate:W = \{15^o}>

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See also

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