1975M2. A bicycle wheel of mass M (assumed to be concentrated at its rim) and radius R is mounted horizontally so it may turn without friction on a vertical axle. A dart of mass mo is thrown with velocity vo as shown above and sticks in the tire.
a. If the wheel is initially at rest, find its angular velocity ω after the dart strikes.
b. In terms of the given quantities, determine the ratio:
> final kinetic energy of the system
> initial kinetic energy of the system