A uniform cylindrical turntable of radius 1.80 m and mass 25.2 kg rotates counterclockwise in a horizontal plane with an initial angular speed of 4pi rad/s. The fixed turntable bearing is frictionless. A lump of clay of mass 2.41 kg and negligible size is dropped onto the turntable from a small distance above it and immediately sticks to the turntable at a point 1.70 m to the east of the axis.
(a) Find the final angular speed of the clay and turntable. Magnitude in rad/s and direction (clockwise or counterclockwise)
b) Is mechanical energy of the turntable-clay system constant in this process? Yes or No ? What, if any, is the change in internal energy? in Joules
(c) Is momentum of the system constant in this process? Yes or No? What, if any, is the amount of impulse imparted by the bearing? magnitude in kg · m/s direction(North or South)