Assume that the rotor of a synchronous motor is stationary. When a pair of rotating stator poles sweeps across the stationary rotor poles at synchronous speed, the stator poles will tend to rotate the rotor in one direction and then in the other direction. As a result, the rotor experiences a torque first in one direction and then in the other. However, the rotor has high inertia and the stator field slides by so fast that the rotor cannot follow it. As a result, the rotor cannot move and hence the resultant starting torque is zero.
But, if the rotor poles are rotated by some external means at such a speed that they interchange their positions along with the stator poles, then the rotor will experience a continuous unidirectional torque.
Consider the stator magnetic field is rotating in clockwise direction at synchronous speed and the rotor is also rotated in the clockwise direction by some external prime mover at such a speed that the rotor poles interchange their positions along with the stator poles.
Now, suppose at any instant the stator and rotor poles are in the position as shown in Figure-1. From Figure-1, it can be seen that the rotor will experience a torque in clockwise direction due to magnetic attraction between the poles NS & SR and SS & NR.
After a period of half-cycle (see Figure-2), the polarities of the stator poles are reversed and at the same time the rotor poles also interchange their positions because the rotor poles are being rotated by an external means at such a speed that they interchange their positions along with the stator poles. The result is that again the rotor experience a torque in the clockwise direction due to the attraction between the poles SS & NR and NS & SR. Therefore, a continuous unidirectional torque acts on the rotor and moves the rotor in the clockwise direction.
Under this condition, the poles on the rotor always face stator poles of opposite polarity and hence a strong magnetic attraction is established between them. This force of attraction magnetically locks the rotor and stator poles together (called magnetic locking). Consequently, the rotor is virtually pulled into step with the speed of rotating magnetic field of the stator (i.e., synchronous speed).
Now, if the external prime mover driving the rotor is removed, the rotor will continue to rotate at synchronous speed in the same direction because the rotor poles are magnetically locked up with stator poles. Also, due to this magnetic locking between the stator and the rotor poles, a synchronous motor runs at the speed of the rotating magnetic field, i.e., synchronous speed.