If an external force, FF$,$ acts on a rigid body, the work, UFUF, done by the force when it moves along a path ss is defined asUF$=$rF$$dr$=$sFcosdsUF$=$rF$$dr$=$sFcosdswhere is the angle between the force and the object's direction of motion and rr is the position vector that points to the object as it moves along path ss$.$

Suppose that after a certain time, tLtL$,$ the string has been pulled through a distance LL$.$ What is $2$$2,$ the final rotational speed of the wheel?

What is PP$,$ the instantaneous power delivered to the wheel via the force FF at time t$=0$t$=0?$