Final answer:
The problem requires understanding the conservation of angular momentum to calculate the new angular velocity of a merry-go-round when a child moves from the edge to the center.
Step-by-step explanation:
The question involves applying concepts of rotational motion and the conservation of angular momentum in Physics. Initially, three children are on the edge of a merry-go-round which has a radius and is spinning at a certain angular velocity. When one child moves to the center, the system's total angular momentum must remain constant, provided there is no external torque applied. Since angular momentum (L) is the product of the moment of inertia (I) and the angular velocity (ω), when a child moves towards the center, the moment of inertia decreases. To conserve angular momentum, the merry-go-round's angular velocity must increase.