Pool Pump Motor Question

If the winding is bad, the motor is dead.

Capacitor-start and capacitor-run motors put the capacitor in series with a second winding. The capacitor causes a phase shift in the current in the second winding so that the magnetic fields of the (unshifted) main winding and the second winding (added together) rotates. A split phase motor gets the phase shift by making the second winding higher resistance or higher inductance, without a capacitor.

But all of these methods need the second winding to work. With one single winding, there is no rotating magnetic field, just a pulsating one. That will keep the motor rotating once started, but won't start it. A capacitor on the main winding will cause a phase shift with respect to incoming power, but there's still no rotating field.

He's dead, Jim - unless you get a motor shop to repair or rewind the start winding.

Dave