(a) A child stands at the centre of a turntable with his two arms outstretched. The turntable is set rotating with an angular speed of 40 rev/min. How much is the angular speed of the child if he folds his hands back and thereby reduces his moment of inertia to 2/5 times the initial value? Assume that the turntable rotates without friction. (b) Show that the child’s new kinetic energy of rotation is more than the initial kinetic energy of rotation. How do you account for this increase in kinetic energy?
The angular speed of the child after folding his hands back is 100 rev/min.
The new kinetic energy is 2.5 times the initial kinetic energy. The increase in kinetic energy is accounted for by the work done by the child in folding his arms back against the centrifugal force.
Explanation
This question tests the principle of conservation of angular momentum and its relation to rotational kinetic energy. When no external torque acts (frictionless turntable), angular momentum is conserved. However, kinetic energy is not conserved because the child does internal work to pull his arms inward.