I don't want to be a voice of gloom, but the windings look a bit burned in your picture. What does it smell like? Perhaps measure continuity across the windings - if there is none, you know it broke as you took it apart (that sounds like my 14-yr-old-self - 'it just broke, Dad'
). Induction motors are on my mind at the moment - I don't think the grinders I use here have a centrifugal start-run switch, so you may have a start-winding with a capacitor on it, assuming this is single-phase. If it is 3-phase, perhaps it will run with one phase broken, but it would perhaps hum quite a lot!
It is difficult to repair things like this where the motor fits into a casing, and a general-purpose motor is hard to fit. If this one is no good and spares cannot be found, I wonder if you can drive the rotor from an external motor using a belt. But this is getting a bit OT for this forum and involves brutality with an angle grinder