A switch operated by rotation is called rotary switch. These are often chosen when more than 2 positions are needed, such as a three or four speed fan reception or channel reception switch.
A rotary switch consists of a spindle or "rotor" that has a contact arm or "spoke" which projects from its surface like a cam. It has an array of terminals, arranged in a circle around the rotor, each of which serves as a contact for the "spoke" through which any one of a number of different electrical circuits can be connected to the rotor.