Question

Two children with identical mass sit on a uniformly rotating merry-go-round. One of them sits close to the axis, and the other sits close to the edge. Consider their angular velocities, rotational inertia and angular momenta about the merry-go-round’s axis. Which of the following is a true statement?

A. The children have the same angular velocity, but different rotational inertia and angular momenta.

B. The children have the same angular velocity and angular momentum, but different rotational inertia

. C. The children have the same angular velocity, rotational inertia, and angular momentum.

D. The children have different angular velocities, rotational inertia, and angular momenta.

Answer 1

angular velocity will be same because angle rotated by both children will be same in same time as both are opposite to each other.

moment of inertia will be differet and given as I=MR^2, here mass is same for both but distance from axis R is different for both, that's why moment of inertia will be different for both.

angular momentum is given by L= IW, as moment of inertia I is different for both that's why angular momentum will be different for both children.

so, option A, The children have the same angular velocity, but different rotational inertia and angular momenta.

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