I still remember an incident with a mirror ball motor when I was in high school. That motor was not much different than the motors in the AC pumps. My friends dad wanted to slow it down, so he but a potentiometer on it. I told him it wouldn't work, but I couldn't remember WHY at that instant.
He turned it on and then turned the pot to slow the motor down and it slowed right down. But just about the time he turned to tell me "See! It works just fine!" the motor burst into flames!
That was also pretty much the instant I remembered WHY you can't do that: If that type motor isn't producing enough power to keep the rotor in phase with the current (aka: turning at the nominal speed) either because the motor is overloaded or the voltage is too low, the voltage waveform and the current waveform get out of sync and windings basically act like a direct DC short.
But not for very long.
