A 4.0 m diameter merry-go-round is rotating freely with an angular velocity of 0

Question

A 4.0 m diameter merry-go-round is rotating freely with an angular velocity of 0.70 rad/s. Its total moment of inertia is 2300 kg·M2. Four people standing on the ground, each of 60 kg mass, suddenly step onto the edge of the merry-go-round. (a) What is the angular velocity of the merry-go-round now?(b) Assume that the people were on it initially (when the angular velocity is 0.70 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?

Explanation / Answer

a) from conservation of angula rmomentum

I1W1 = I2W2

W2 = 2300*0.7/(2300+4*60*2^2)

W2 = 0.49 rad/s

b) w2 = (2300+4*60*2^2)*0.7/2300 = 0.99 rad/s

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