11. A playground merry-go-round has a radius of 3.0 m and arotational inertia of

Question

11. A playground merry-go-round has a radius of 3.0 m and arotational inertia of 600 kg m2. It is initially spinning at 0.80 rad/s when a 20-kg child crawlsfrom the center to the rim. When the child reaches the rim the angular velocity of themerry-go-round is: A) 0.61 rad/s B) 0.73 rad/s C) 0.80 rad/s D) 0.89 rad/s E) 1.1rad/s 11. A playground merry-go-round has a radius of 3.0 m and arotational inertia of 600 kg m2. It is initially spinning at 0.80 rad/s when a 20-kg child crawlsfrom the center to the rim. When the child reaches the rim the angular velocity of themerry-go-round is: A) 0.61 rad/s B) 0.73 rad/s C) 0.80 rad/s D) 0.89 rad/s E) 1.1rad/s

Explanation / Answer

radius R = 3 m rotational inertia I = 600 kg m ^ 2 angular speed w = 0.8 rad / s mass of child m = 20 kg new angular speed   w ' = I w / I ' where I ' = new rotational inertia               = I + m R ^ 2               = 780 kg m ^ 2 So, w ' = 0.61 rad / s

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