A turntable has rotational inertia I and is rotating with angular speed w 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 at right angles to the turntable’s radius, and in the same direction as the turntable’s rotation (see the figure). 15 cm diameter.

Find an expression for v that will result in the turntable’s angular speed dropping to half its initial value.
Find an expression for v that will result in no change in the turntable’s angular speed.
Find an expression for v that will result in the angular speed doubling.