They will always run somewhat lower frequency due to this 'slip' otherwise they would run at exactly 3600rpm (2 pole 60hz) or 1800rpm (4 pole 60hz).
There is a way to create synchronism, a circuit detects when the slip frequency is approaching and injects a DC field into the rotor, hence locking the rotor to the rotating field, but not in your average motor.
A 1 ph motor will never start without a phase-shifted start winding, due to no rotating field at switch on.
Also a Standard motor rotors appear to be a solid chunk of metal, but actually has windings, these are conductive bars embeded in the rotor and connected with shorted turns at the end of the rotor, they used to comprise of copper many years ago, but now are generally aluminum composition.
Hence 'Squirrel Cage' motor
This is also why the high current is caused by a stalled motor, there is full current reflected back from the shorted turns on the rotor to the stator.