A 21-kg child starts at the center of a playground merry-go-round that has a radius of 3.5 m and rotational inertia of 500 kg⋅m2 and walks out to the edge. The merry-go-round has a rotational speed of 0.20 s−1 when she is at the center.

Question

What is its rotational speed when she gets to the edge?

Answer 1

This is a conservation of angular momentum problem.
Now, the formula for angular momentum is:
L = Iw
So basically, L before = L after:
I1w1 = I2w2
The trick to solving these is to figure out what the change in moment of inertia is, and then apply the concept of conservation of angular momentum to it.
With a person on a merry-go-round, the moment of inertia would be the moment of inertia of the person plus the moment of inertia of the merry-go-round.
In this case the person starts at the center of the rotating merry-go-round, and so I think we are to say their moment of inertia is zero or negligible (it would be small), but then they move to the outside edge of the merry-go-round, and in the after picture, have a significant moment of inertia. The moment of inertia of the merry-go-round is the same before and after and given as 670 kgm2