You have to sort of visualize the composite EM Field from the 3 phases. The 3 phases are offset 120 degrees from each other. Imagine 3 electromagnets in a straight line. Each magnet is connected to one of the phases. If the first one to the left is at peak (max magnetic field is over it), the other 2 are at less than peak, but the current in the left magnet is falling while the current in the center and right are building. The right is farther behind===> Center reaches peak first (Now the peak magnetic field is over the center). But the center current is falling while the right continues to build to peak. Now the peak magnetic field is over the right and the left has been building again ===> The magnetic field moves over the left again and the cycle repeats.
Now bend those 3 magnets into a circle ===> rotating field.
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Because the slip angle between magnetic fields decreases as the rotor comes up to speed.
Shading coils provide a phase shift between the magnetic field of the rotor and stator, which is necessary to get the motor spinning.
So as to start the motor because reactive power helps create the magnetic fields in rotor.
Current carrying conductor kept in a magnetic field gets deflected. This is the basic principle. In short Lorentz force causes the rotation
To create rotating magnetic field inside motor stator and it is done by capacitor. current drawn by motor running winding is lagging in nature when capacitor is connected in series with starting winding then the phase angle of running winding current and starting winding currents changes which creates a rotating magnetic field and motor is able to run.