tem 11 A 47-kg child stands on the edge of a 350-kg playground merry-go-round th

Question

tem 11 A 47-kg child stands on the edge of a 350-kg playground merry-go-round that is turning at the rate of 1 rev every 2.2 s. He then walks to the center of the platform. Part A If the radius of the platform is 1.5 m, what is its rotational speed once he arrives at the center? Assume that the platform is a uniform disk, and the child is "point-like", that is, his dimensions are so small compared to the platform size, that he can be considered to be a point-mass. Hints Submit My Answers Give Up

Explanation / Answer

Consider conservation of momentum.

initial momentum = final momentum

Write the expression for momentum.

Momentum= moment of inertia * angular velocity

Write the expression for moment of inertia.

Moment of inertia of the merry go round = (1/2) * mass * radius^2

moment of inertia of the merry go round = 0.5 * 350 * 1.5^2

Given initial angular velocity (w_i) = 1 / 2.2 rev/sec or 2.8559 rad/sec.

Consider the conservation of momentum.

(I+mr^2)*w_i=I*w_f

((1/2)* 350 * 1.5^2 + 47 * 1.5^2) * 2.8559 = (1/2) * 350 * 1.5^2 *w_f

final rotational speed(w_f) = 3.6229 rad/sec

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