The motion of a child on a merry-go-round is circular in nature. When the child sits on the merry-go-round, they move around a central point, revolving in a circular path. The ride spins around a fixed axis at its center, causing the child to continuously move in a circular motion. This rotational movement, where the child travels in a circular path around the center of the merry-go-round, defines the circular motion experienced on the ride.