A playground merry-go-round has radius 2.50 m and moment of inertia 2000 kg⋅m2 about a vertical axle through its center, and it turns with negligible friction.
part a
A child applies an 23.5 N force tangentially to the edge of the merry-go-round for 22.0 s . If the merry-go-round is initially at rest, what is its angular speed after this 22.0 s interval?
part b
How much work did the child do on the merry-go-round?
part c
What is the average power supplied by the child?
a) torque = F r
I * alpha = F r
F r = I (wf - wi) / t
F r = I wf / t
wf = F r t / I = (23.5 * 2.5 * 22) / (2000)
= 0.646 rad/s
b) W = 1/2 I wf2
= 1/2 * 2000 * 0.6462
= 417 J
c) P = W / t
= 417.3 / 22 = 18.9 W
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