What kind of motion is a merry go round?

The motion of a merry go round is circulatory ie. In a circular motion.
Circular motion is defined as the movement of an object along the circumstances of a circle or a rotation along a circular path.

Example of such is the circular motion of a moving ceiling fan, the blades of the fan are moving in a circular manner another example is a stone tied to a rope and swung in a circular manner. For an object to move in a circular motion, there most be an inward force acting upon the object and causing the object to seek the center of the circle.

The merry go round has a spinning motion and is a good example of centrifugal force. When you sit on the edge you feel dizzier than if you sit in the middle. This is because your inner ear helps you keep your balance, and when it's disturbed by a spinning force you feel dizzy.

There's a greater force on the edge, and therefore you get dizzier. This feeling of being pushed outward is centrifugal force. Centrifugal force is different from centripetal force and the two should not be confused, but often are.