Speed Controlling an AC motor
Not with this kind of motor. They count on a known phase shift (that’s the split-phase part) and frequency to run properly.

Chopping the AC as you propose adds harmonic distortion to that drive waveform. As you clip the waveform more, the motor will run rough, might slow down a bit, then stall.

A ‘universal’ motor on the other hand can be controlled in the way you propose.