Consider a person who spins a large grindstone by placing her hand on its edge and exerting a force through part of a revolution as shown in Figure 10.16. In this example, we verify that the work done by the torque she exerts equals the change in rotational energy. 

(a) How much work is done if she exerts a force of 200 N through a rotation of ? The force is kept perpendicular to the grindstone’s 0.320-m radius at the point of application, and the effects of friction are negligible.

(b) What is the final angular velocity if the grindstone has a mass of 85.0 kg? 

(c) What is the final rotational kinetic energy? (It should equal the work.)

Strategy

To find the work, we can use the equation net W =(net τ)θ. We have enough information to calculate the torque and are given the rotation angle. In the second part, we can find the final angular velocity using one of the kinematic relationships. In the last part, we can calculate the rotational kinetic energy from its expression in

Transcribed Image Text:

F α r