Suppose a child walks from the outer edge of a rotating merry-go round in towards the center of rotation. Does the angular velocity of the merry-go-round increase, decrease, or remain the same?

Increases.

Explanation:

Angular velocity is defined as the time rate of change of the distance of the circular motion in rad/s.

As the child walks from the outer edge to the center, the moment of inertia, I is the sum of the moment of inertia of the merry go round and the child.

As the child walks inwardly, the moment of inertia decreases and so the net moment of inertia decrease. Hence, final angular velocity increases.

The final angular velocity can be calculated from the definition of angular momentum,

L = Iω.