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A track is mounted on a large wheel that...

A track is mounted on a large wheel that is free to turn with neigligible friction about a vertical axis (Fig). 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 `v` with respect to the track. What is the wheel's angular speed if its mass is `m` and its radius is `r` ? (Treat it as a hoop, and neglect the mass of the spokes and hub).
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