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.

A man stands on a rotating platform, with his arms stretched horizontally holding a 5 kg weight in each hand. The angular speed of the platform is 30 revolutions per minute. The man then brings his arms close to his body with the distance of each weight from the axis changing from 90cm to 20cm. The moment of inertia of the man together with the platform may be taken to be constant and equal to 7.6 kg m^2 :- What is his new angular speed? (Neglect friction.)

A man stands on a rotating platform, with his arms stretched horizontally holding a 5 kg weight in each hand. The angular speed of the platform is 30 revolutions per minute. The man then brings his arms close to his body with the distance of each weight from the axis changing from 90cm to 20cm. The moment of inertia of the man together with the platform may be taken to be constant and equal to 7.6 kg m^2 :- Is kinetic energy conserved in the process? If not, from where does the change come about?

A boy standing on a stationary lift (open from above) throws a ball upwards with the maximum initial speed he can, equal to 49 m s^-1 . How much time does the ball take to return to his hands? If the lift starts moving up with a uniform speed of 5 m s^-1 and the boy again throws the ball up with the maximum speed he can, how long does the ball take to return to his hands ?

A 70 kg man stands in contact against the ineer wall of a hollow cylindrical drum of radius 3 m rotating about its vertical axis with 200 rev//min . The coeffcient of friction between the wall and his clothing is 0.15. What is the minimum rotational speed of the cylinder to enable the man of remain stuck to the wall ( without falling) when the floor ids suddenly removed?

The oxygen molecule has a mass of 5.30 xx 10^-26 kg and a moment of inertia of 1.94xx10^-46 kg m^2 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.