Simultaneous Rotational and Translational Motions

If a point in a rigid body is not fixed, it can possess rotational motion as well as translational motion. The general motion of a rigid body consists of both these motions. For example, the motion of an automobile wheel on a plane horizontal surface.

The kinetic energy of translation is

(KE)tr = ½Mv_cm²

The kinetic energy of rotation is

(KE)_rot = ½Iω²

The total energy of the body due to translation and rotation is the sum of these two kinetic energies.