(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?

A disc of radius R is rotating with an angular speed \(\omega \), about a horizontal axis. It is placed on a horizontal table. The coefficient of kinetic friction is \({ \mu }_{ k }\).
(i) What was the velocity of its centre of mass before being brought in contact with the table?
(ii) What happens to the linear velocity of a point on its rim when placed in contact with the table?
(iii) What happens to the linear speed of the centre of mass when disc is placed in contact with the table?
(iv) Which force is responsible for the effect in (ii) and (iii)?
(v) What condition should be satisfied for rolling to begin?
(vi) Calculate the time taken for the rolling to begin.

A solid sphere rolls down two different inclined planes of the same heights but different angles of inclination.
(a) Will it reach the bottom with the same speed in each case?
(b) Will it take longer to roll down one plane than the other?
(c) If so, which one and why?

The oxygen molecule has a mass of 5.30 × 10^-26 kg and a moment of inertia of 1.94 × 10^-46 kg m² about an axis through its centre perpendicular to the lines joining the two atoms. Suppose the mean speed of such a molecule in a gas is 500 m/s and that its kinetic energy of rotation is two thirds of its kinetic energy of translation. Find the average angular velocity of the molecule.