Halliday, Resnick & Walker — Rolling, Torque, and Angular Momentum: Problem 51

51 A wheel of rotational inertia \(0.100 \text{ kg}\cdot\text{m}^2\) is rotating about a shaft at an angular speed of \(160 \text{ rev/min}\). A second wheel is set into rotation at \(300 \text{ rev/min}\) and mounted on the same shaft, so that the wheels couple together. Their final angular speed is \(200 \text{ rev/min}\). Find (a) the rotational inertia of the second wheel and (b) the change in the rotational kinetic energy of the system due to the rubbing of wheel on wheel.