Speed of Synchronous motor determined by frequency, but how about current?
Clearly you have to apply power to the motor and you have to apply enough supply voltage to overcome motor losses. Once you do that the motor works synchronously off-load but when mechanical load is applied to the shaft there has to be enough current in the source to be able to supply mechanical power and still overcome the losses in the motor.

As a footnote, synchronous speed means exactly that but as a mechanical load increases, the rotating shaft "slips" a small angle to accommodate that change in load and draw more current.