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A uniform cylindrical turntable of radius 2.00 m and mass 26.8 kg rotates counterclockwise in a horizontal plane with an initial angular speed of 4? 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 1.90 m to the east of the axis.

(a) Find the final angular speed of the clay and turntable.

(b) Is mechanical energy of the turntable-clay system constant in this process?

(c) Is momentum of the system constant in this process?

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