Final answer:
The horse on the outside of the merry-go-round moves faster in terms of linear speed, but both the inside and outside horses have the same angular velocity. When a child moves inward on the merry-go-round, the angular velocity increases due to conservation of angular momentum.
Step-by-step explanation:
The question of which horse moves faster on a merry-go-round depends on the definition of speed being used. If we're discussing linear speed, then the horse on the outside near the outer rail moves faster because it covers a larger circumference in the same period of time as the horse on the inside. However, both horses spin around the center at the same angular velocity; they complete the same number of revolutions in the same amount of time.
Regarding the effect of a child moving from the outer edge to the inside, the angular velocity of the merry-go-round would increase. This is due to the conservation of angular momentum, and the moment of inertia decreases if the mass is closer to the axis of rotation, thus increasing the angular velocity if no external torque is applied.