A playground merry-go-round has radius 2.10 m and moment of inertia 2100 kg · m

Question

A playground merry-go-round has radius 2.10 m and moment of inertia 2100 kg · m2 about a vertical axle through its center, and it turns with negligible friction.

(a) A child applies a 23.0-N force tangentially to the edge of the merry-go-round for 19.0 s. If the merry-go-round is initially at rest, what is its angular speed after this 19.0-s interval?
rad/s

(b) How much work did the child do on the merry-go-round?
J

(c) What is the average power supplied by the child?
W

A playground merry-go-round has radius 2.10 m and moment of inertia 2100 kg·m2 about a vertical axle through its center, and it turns with negligible friction. (a) A child applies a 23.0-N force tangentially to the edge of the merry-go-round for 19.0 s. If the merry-go-round is initially at rest, what is its angular speed after this 19.0- s interval? rad/s (b) How much work did the child do on the merry-go-round? (c) What is the average power supplied by the child?

Explanation / Answer

a) w = FRt/I = 23 x 2.1 x 19/2100 = 0.437 rad/s

b) W = 0.5 Iw2 = 0.5 x 2100 x 0.437 x 0.437 = 200.52 J

c) avg. power = 200.52/19 = 10.55355 W

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