The work-energy theorem for rotational motion is analogous to the work-energy theorem in translational motion. It states that the net work done by an external force to rotate a rigid body equals the change in the object's rotational kinetic energy. The power delivered is simply the time derivative of the work done; therefore, power is the dot product of torque and angular velocity. This relation is analogous to power in translational motion, which is given by the dot product of force and velocity. It is assumed that frictional force is absent here; however, this is not always the case for a real system. For example, an airplane's engine does work to set the propeller into a spinning motion. However, air friction and the friction between the mechanical parts of the engine lead to inevitable losses, as the work done by the engine translates into the change in rotational kinetic energy of the propeller. Therefore, even after the propeller gains the final desired angular velocity (and hence the desired rotational kinetic energy), the engine still needs to work to balance the opposing forces, which could otherwise slow down the spinning propeller.
This text is adapted from Openstax, University Physics Volume 1, Section 10.8: Work and Power for Rotational Motion.
