Question

A 20-kg child running at 2.0 m/s jumps onto a playground merry-go-round that has inertia 180 kg and radius 1.6 m. She is moving tangent to the platform when she jumps, and she lands right on the edge. Ignore any friction in the axle about which the platform rotates. What is the rotational speed of the merry-go-round and the child if the merry-go-round started from rest? Express your answer with the appropriate units.

Answer 1

Solution:

Merry-go-rounds are usually modeled as uniform disks,
I_m = 1/2Mr²
and when the boy is at the edge, you also need to count that:
I_b = mr²
so the total moment of inertia with the boy at the edge is
I = (M/2 + m)r²

so
Using coservation of angular momentum,

mvr = (M/2 + m)r²

= m*v / (M/2 + m)*r = 2*m*v / (M + 2m)*r

Sunstitute the values,

= 20*2/[180/2 +20]*1.6

= 0.2272727

= 0.230 rad/s.

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