A uniform cylindrical turntable of radius m and mass kg rotates counterclockwise in a horizontal plane with an initial angular speed of π rad/s. The fixed turntable bearing is frictionless. A lump of clay of mass kg and negligible size is dropped onto the turntable from a small distance above it and immediately sticks to the turntable at a point m to the east of the axis. (a) Find the final angular speed of the clay and turntable. (b) Is the mechanical energy of the turntable–clay system constant in this process? Explain and use numerical results to verify your answer. (c) Is the momentum of the system constant in this process? Explain your answer.