Chapter 11, Problem 53P

A turntable has rotational inertia I and is rotating with angular speed ω about a frictionless vertical axis. A wad of clay with mass m is tossed onto the turntable and sticks a distance d from the rotation axis. The clay hits horizontally with its velocity $\stackrel{\to }{v}$ at right angles to the turntable’s radius, and in the same direction as the turntable’s rotation (Fig. 11.17). Find expressions for v that will result in (a) the turntable’s angular speed dropping to half its initial value, (b) no change in the turntable’s angular speed, and (c) the angular speed doubling.