A 30 kg child is sitting on the outer edge of a 100 kg carousel with a radius of

Question

A 30 kg child is sitting on the outer edge of a 100 kg carousel with a radius of 2.0 m. (The carousel can be modeled as a disk and assume it rotates without friction on its axis, the child can be modeled as a point mass) The carousel is initially at rest.

a) What is the moment of inertia of the carousel and child?

b) The child pushes against the ground with a force of 25 N to get the carousel moving. What is the resulting torque?

c) What is the resulting angular acceleration of the carousel and child?

d) What is the kinetic energy of the child and carousel after 10 s?

Explanation / Answer

Part A)

I = .5MR2 + mr2

I = .5(100)(2)2 + (30)(2)2

I = 320 kg m2

Part B)

Torque = Fr

Torque = (25)(2) = 50 Nm

Part C)

Torque = I(alpha)

50 = (320)(alpha)

alpha = .156 rad/s2

Part D)

wf = wo + (alpha)t

wf = 0 + (.156)10

wf = 1.56 rad/s

KE = .5Iw2

KE = (.5)(320)(1.56)2

KE = 391 J

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