## The Equations of Rotational Motion

The equations of linear motion are

Where u=initial velocity v=final velocity a=acceleration t=time s=displacement | |

These equations have analogous equations for motion in a circle. These equations arise directly from the equation arc length = radius*angle ( in radians) or

If we differentiate s= r %theta with respect to time we havewhereis called the angular velocity and differentiating again gives awhereis called the angular acceleration.

Substituteandin the equations of motion to get

Divide the first, second, third and fifth byand the fourth byto get