Single-phase AC motor only has one winding, the rotor is a squirrel-cage. When the single-phase sinusoidal current goes through the stator windings, the motor will produce an alternating magnetic field, the strength and direction of the magnetic field change as sine with time, but in the spatial orientation, it is fixed, so the magnetic field is also called alternating pulsating magnetic field. This alternating pulsating magnetic field can be decomposed into two rotating magnetic field at the same rotational speed and the opposite direction. When the rotor is stationary, the two rotating magnetic fields generate two rotors with equal-sized and opposite direction in rotor, such that the synthesis of torque is zero, so the motor can not be rotated. When we use the external force to rotate the ac motor in one direction (eg clockwise rotation), then the action of cutting magnetic flux between rotating magnetic field of the rotor with a clockwise direction of rotation becomes smaller; the action of cutting magnetic flux between rotating magnetic field of the rotor and the counter-clockwise direction becomes larger. Thus breaking the balance, total electromagnetic torque generated by the rotor will no longer be zero, the rotor will rotate along the direction of push.
For single-phase motors can automatically rotate, you can add a starter winding in the stator, starting winding and primary winding have 90 degrees difference in the space, start winding should cascade a suitable capacitor, so that the current is approximately 90 degrees difference in phase with the current of primary winding, that is the phase separation principle. So that the two types of current differ 90 degrees in the time flow into the two winding differ 90 degrees in space, will produce (two-phase) rotating magnetic field in space. Under the action of this rotating magnetic field, the rotor will automatically start, after starting, with the help of centrifugal switch or other automatic control device installed on rotor turn off the starting winding, only the main winding work during normal operation. So, the start winding can be made short work. But there is a lot of time, do not switch off the start winding, such motors are called capacitive single-phase motors, we can reverse the direction of single phase ac motor by changing the position of the capacitor connected in series.