Halliday, Resnick & Walker — Rotation: Problem 61

61 Disks A and B each have a rotational inertia of $0.300 \text{ kg} \cdot \text{m}^2$ about the central axis and a radius of $20.0 \text{ cm}$ and are free to rotate on a central rod through both of them. To set them spinning around the rod in the same direction, each is wrapped with a string that is then pulled for $10.0 \text{ s}$ (the string detaches at the end). The magnitudes of the forces pulling the strings are $30.0 \text{ N}$ for disk $A$ and $20.0 \text{ N}$ for disk $B$. After the strings detach, the disks happen to collide and the frictional force between them brings them to the same final angular speed in $6.00 \text{ s}$. What are (a) magnitude of the average frictional torque that brings them to the final angular speed and (b) the loss in kinetic energy as that torque acts on them? (c) Where did the “lost energy” go?