per minute. So
I'm going to oversimplify a bit here but here's the basic idea:
In a conventional induction motor, the stator creates a magnetic field that "rotates" around the rotor. As the field crosses the rotor, it induces a current in the rotor, which causes the rotor to develop its own magnetic field. The rotor field is attracted & repelled by the rotating stator field and causes the rotor to turn. Here's the part that you need to wrap your mind around: The stator field rotates or fluctuates according to line frequency. If the rotor rotates at the RPM that the line frequency would indicate, then the stator magnetic field would not cross the rotor windings, because as the stator field rotated, the rotor would be rotating right along with it. Since there would then be no induced current or magnetic field in the rotor, the motor would be operating at 0 (zero) torque.
Of course there is always some load on a motor, even when not connected to anything there is some drag in the bearings. So the load tends to slow down the rotor, which means that the stator mag field starts crossing the rotor more frequently, inducing more current, etc.
The speed listed on a motor data plate is the RPM at full load. A 1.5 hp table saw motor, for instance , might spin at "almost" 3600 RPM when it's just sitting there running. But when you start ripping some 8/4 maple, it slows down, draws more current and produces more torque. At it's full design load, it might be spinning at say 3450 RPM.
Now, there is a type of motor called a "synchronous" motor and it does rotate at synchronous speed. Unlike an induction motor, though, a synch. motor has DC current supplied to windings in the rotor to create fixed magnetic fields, relative to the rotor. Theoretically permanent magnets could be used. These synchronous motors are usually
3 phase, and the stator windings are arranged more or less the same as in an induction motor, causing a rotating magnetic field. Instead of depending on this field inducing current and a magnetic field in the rotor, though, the magnetic fields of the rotor want to chase the rotating stator field around. No induction is required to generate the rotor field, so the rotor doesn't "slip" like it does in an induction motor.