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

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