A child is standing on the edge of a merry-go-round that has the shape of a disk, as shown in the figure above. The mass of the child is 40 kilograms. The merry-go-round has a mass of 200 kilograms and a radius of 2.5 meters, and it is rotating with an angular velocity of ω = 2.0 radians per second. The child then walks slowly toward the center of the merry-go-round. What will be the final angular velocity of the merry-go-round when the child reaches the center ? (The size of the child can be neglected)

Question

G1 Physics · Accepted Answer

Conserve angular momentum about the vertical axis. Initially the total moment of inertia is ½MR² + mR²; finally the child is at the centre, so it is ½MR². With M = 200 kg, m = 40 kg, R = 2.5 m and initial angular speed 2 rad/s, the final angular speed is 2.8 rad/s. Hence D.