A child standing on the edge of a free> spinning merry-go-round moves quick the

Question

A child standing on the edge of a free> spinning merry-go-round moves quick the center. Which one of the following statements is necessarily TRUE concerning this event and why? The angular speed of the system decreases because the moment of inertia of the system has increased. The angular speed of the system increases because the moment of inertia of the system has increased. The angular speed of the system decreases because the moment of inertia of the system has decreased. The angular speed of the system increases because the moment of inertia of the system has decreased. The angular speed of the system remains the same because the net torque on the merry-go-round is zero.

Explanation / Answer

angular momentum L = IW

here I is the total moment of inertia of the both merry go round and the girl. Moment of inertia of the girl is decreased when she approched the cerntre ( since I = m r2). Hence total moment of inertial will be decreased.

Angular momentum is conserved. so angular speed w is inversely vary with moment of inertia; i.e lowr is the moment of inertia, higher is the angular speed.so the anser is D.

i.e. The angular speed of the system increases because the moment of inertia of the system has decreased

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