Question

A circular platform is mounted on a frictionless vertical axle. Its radius R = 2 m and its moment of inertia about the axle is 200 kg m². It is initially at rest. A 50 kg man stands on the edge of the platform and begins to walk along the edge at the speed of 1 ms⁻¹ relative to the ground. Find the angular velocity of the platform and time taken by man relative to platform.

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?