Question

Two children (m = 34.0 kg each) stand opposite each other on the edge of a merry-go-round. The merry-go-round, which has a mass of 1.60 ✕ 10^2 kg and a radius of 1.6 m, is spinning at a constant rate of 0.34 rev/s. Treat the two children and the merry-go-round as a system. Both children walk half the distance toward the center of the merry-go-round. Calculate the final angular speed of the system.

Answer 1

I initial=Idisk+Ikida+Ikidb
and same for final If. just remember the Ikids is 1/2 mr^2, and the second r is 1/2 the first.
conservation of angular momentum
Iinitial*wi=Ifinal*wfinal
and you solve for Wfinal.