A horizontal turntable is made to rotate about a fixed vertical axis with constant angular speed . A hollow uniform circular cylinder of mass M and radius a can roll on the turntable. Initially the cylinder is at rest (relative to the turntable), with its centre of mass on the rotation axis, when it is slightly disturbed.
Find the speed of the cylinder when it has rolled a distance x on the turntable. Find also an expression (in terms of x) for the force that the turntable exerts on the cylinder.