A playground merry-go-round, made in the shape of a solid disk, has a diameter o

Question

A playground merry-go-round, made in the shape of a solid disk, has a diameter of 2.550 m and a mass of 352.3 kg. Two children, each of mass 30.20 kg, sit on opposite sides at the edge of the platform. Approximate the children as point masses. Part 1 out of 2 (a) What torque is required to bring the merry-go-round from rest to 24.00 rpm in 19.90 s? N ·m

b) If two other bigger children are going to push on the merry-go-round rim to produce this acceleration, with what force magnitude must each child push?
_____ N

Explanation / Answer

a) d = 2.550 m, r = 1.275 m, m = 352.3 kg, m' = 30.20 kg, f = 24 rpm = 0.4 rev/s

I = I1 + I2 = mr2/2 + 2 m' r2 = [352.3*1.2752/2] + [2*30.20*1.2752] = 384.54 kg.m2

w1 = 0 , w2 = 2 pi f = 2 pi * 0.4 = 2.513 rad/s

alpha = (w2 - w1) / t = 2.513 / 19.90 = 0.126 rad/s2

Torque = I * alpha = 384.54 * 0.126 = 48.5 N.m

b) T = F * r = 48.5 N.m

F * 1.275 = 48.5

F = 38.0 N

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