A 4.2 m diameter merry-go-round is rotating freely with an angular velocity of 0

Question

A 4.2 m diameter merry-go-round is rotating freely with an angular velocity of 0.60 rad/s. Its total moment of inertia is 2250 kg.M2. Four people standing on the ground, each of 50 kg mass, suddenly step onto the edge of the merry-go-round.

1. What is the angular velocity of the merry-go-round now? w= ____________________ rad/s

2. Assume that the people were on it initially (when the angular velocity is 0.60 rad/s) and then jumped off in a radial direction (relative to the merry-go-round). What would be the angular velocity of the merry-go-round? w=__________________ rad/s

Explanation / Answer

by conservation of momentum

initial momentum = final momentum

momentum = momentum of inertia * angular velocity

initial momentum = 2250 * 0.6

after four people step into edge new moment of inertia will be

new moment of inertia = 2250 + 4 * mass of each person * radius^2

new moment of inertia = 2250 + 4 * 40 * 2.1^2

final momentum = (2250 + 4 * 40 * 2.1^2) * new angular velocity

2250 * 0.6 = (2250 + 4 * 40 * 2.1^2) * new angular velocity

1) new angular velocity = 0.4567 rad/sec

in case when people were initially on the go round

(2250 + 4 * 40 * 2.1^2) * 0.6 = 2250 * new angular velocity

2) new angular velocity = 0.788 rad/sec

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