Question

A toy train track is mounted on a large wheel that is free to turn with negligible friction about a vertical axis (see the figure). A toy train of mass m = 2.5 kg is placed on the track and, with the system initially at rest, the electrical power is turned on. The train reaches a steady speed v = 0.4 m/s with respect to the track. What is the angular velocity ω of the wheel, if its mass is M = 4.50 kg and its radius R = 0.6 m? (Treat the wheel as a hoop, and neglect the mass of the spokes and hub.)