Question

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?

Answer 1

a) torque = F r

I * alpha = F r

F r = I (w_f - w_i) / t

F r = I w_f / t

w_f = F r t / I = (23.5 * 2.5 * 22) / (2000)

= 0.646 rad/s

b) W = 1/2 I w_f²

= 1/2 * 2000 * 0.646²

= 417 J

c) P = W / t

= 417.3 / 22 = 18.9 W