question_answer 23)

A man stands on a rotating platform, with his arms stretched horizontally holding a 5kg 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 90 cm to. 20 cm. The moment of inertia of the man together with the platform maybe taken to be constant and equal to . Ans.     (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 ?  

Answer:

(a) Total initial moment of inertia,  of man and platform                 + M.I. of two 5 kg weights     Initial angular speed,   Total final moment of inertia,   By the principle of conservation of angular momentum,   or            or            . (b) . Thus the final K.E. is about twice the initial K.E. i.e., K.E. is not conserved in the process. The increase in K.E. is due to the internal energy the man uses in bringing his arms closer to his body.