rotate on (something)
1. To turn on or spin around a particular axis or central point. The damage from the accident resulted in the wheels no longer rotating on the front axle properly.
2. To cause something to turn on or spin around a particular axis or central point. In this usage, a noun or pronoun is used between "rotate" and "on." If you rotate the ball on the tip of your finger quickly enough, the centripetal force will keep it balanced in place.
rotate on something
to spin on something; to pivot on something. This wheel rotates on this little red jewel on the main frame of the watch. The record rotates on this device, which is called a turntable.