A playground merry-go-round has radius 2.80 and moment of inertia 2000 about a v

Question

A playground merry-go-round has radius 2.80 and moment of inertia 2000 about a vertical axle through its center, and it turns with negligible friction.


Part A
A child applies an 21.0 force tangentially to the edge of the merry-go-round for 23.0 . If the merry-go-round is initially at rest, what is its angular speed after this 23.0 interval?
w =_______________rad/s


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Part B
How much work did the child do on the merry-go-round?
W=_____________J




Part C
What is the average power supplied by the child?
P =___________W

Explanation / Answer

angular accelaration = torque/moment of inertia

= (21 x 2.8)/2000

= 0.0294rad/s2

hence after 23 sec,

a) = t

= 0.0294 x 23 = 0.6762rad/s

b) work done =

= (1/2)t2

= (1/2)(0.0294)(232)

= 7.77rad

hence W = (21 x 2.8) x 7.77

W = 457.24J

c) power = W/t

P = 457.24/23

P = 19.88W

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