# Sol HW9Q9 says I(initial)*omega(initial)=I(final)*omega(final) What concept is this? conservation of what?

This question is about the conservation of angular momentum, which is defined as $$\vec L=\vec r \times \vec P=I\vec \omega.$$
This question is similar to the inelastic collision in linear case, in which the momentum before and after are the same and after the collision, the two objects have the same velocity. In this rotational motion case, the angular momentum $\vec L$ is conserved (be the same before and after collision). Also after hopping on the child and the merry-go-round will rotate together with the same angular velocity, which makes it easier to calculate the angular momentum after the "collision". Note that here you will need to use $I$ instead of mass in the linear motion situations.