Walker, Halliday & Resnick — Rolling, Torque, and Angular Momentum: Problem 47

47 A track is mounted on a large wheel that is free to turn with negligible friction about a vertical axis (Fig. 11-42). A toy train of mass $m$ is placed on the track and, with the system initially at rest, the train's electrical power is turned on. The train reaches speed $0.15 \text{ m/s}$ with respect to the track. What is the wheel's angular speed if its mass is $1.1m$ and its radius is $0.43 \text{ m}$? (Treat it as a hoop, and neglect the mass of the spokes and hub.)