A 78 kg person is standing on the edge of a rotating merry-go-round platform wit

Question

A 78 kg person is standing on the edge of a rotating merry-go-round platform with a 3.0-m radius, 205kg mass and a 1.45 rad/s angular velocity. The person walks toward the center until he is on the verge of slipping, at which point his angular velocity is 2.5 rad/s. Treat the person as a point mass and the merry go round as a uniform disk. A) How far from the center does he make it? B) How much Kinetic energy is lost after he has moved to the center? C) What is his centripetal acceleration after moving toward the center? D) What is the coefficient of static friction between his feet and the merry go round?

Explanation / Answer

I (disk) = mr^2 /2 = 922.5 I (man) = mr^2 = 702 I1w1 = I2w2 (922.5+702) x 1.45 = (922.5 + 78r^2) x 2.5 A) r = 0.5027 m B) KE (lost) = 0.5 ( I1w1^2 - I2w2^2) = 1236 J C) w^2 r = 3.125 rad/s^2 D) umg = mw^2r u = 0.31887

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