Question

A track is mounted on a large wheel that is free to turn with negligible friction about a vertical axis. A toy train of mass m = 0.140 is placed on the track and, with the system initially at rest, the train's electrical power is turned on. The train reaches a steady speed of 0.17 m/s with respect to the track. What is the angular speed of the wheel if its mass is 1.4m and its radius is 0.42 m? (Treat the wheel as a hoop, and neglect the mass of the spokes and hub.)