Question

Assertion (A): Angular momentum of a system is conserved in the absence of external torque. Reason (R): Torque is the time derivative of angular momentum.

(i) What are the factors on which the M.I of a body depends? (ii) When a cat can land on its feet after a fall, which property of Physics is being used by her?

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 minutes. The man then brings his arms close to his body with the distance of each weight from the axis changing from 90 cm to 20 cm. The moment of inertia of the man together with the platform may be taken to be constant and equal to 7.6 kg m². (a) What is his new angular speed? (Neglect friction) (b) Is kinetic energy conserved in the process? If not, from where does the change come about?

(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?