Todd writes:
I have a 3/4 HP pool pump motor that has a centrifugal switch in it.
The start windings have gone bad so it will not start on its own but
will run fine if I "give it a hand" to get started. My question is
can I put a start capacitor on the main windings to get it going? Will
it work? What size capacitor should I try? Capacitor are far cheaper
than pool pumps so giving it a try would be a low bux solution.

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