Physics: Rigid Body Dynamics #1: Centripetal acceleration and moment of inertia

In Rigid Body Statics, the sum of all torques and forces was zero. This meant that both linear acceleration and centripetal acceleration are equal to zero, and thus we were not concerned with them:

In Rigid Body Dynamics, however, there is a Torque. Thus, an expression relating torque with centripetal acceleration must be derived:

This is the main idea behind Rigid Body Dynamics.