In a lecture demonstration, a toy train track is mounted on a large
wheel that is free to turn with negligible friction about a vertical
axis; see Fig. 10-25.
A toy train of mass m is placed on the track and, with the system initially at rest, the electrical power is turned on.
train reaches a steady speed v with respect to the track. What is the
angular velocity of the wheel, if its mass is M and its radius R?
(Neglect the mass of the spokes (wires) of the wheel.)