Two probable causes:
1. Bearings are dry or worn.
2. Centrifugal start switch is sticking. May or may not have one, it's a set of contacts with fly weights on it that keep the motor on the start winding until the speed flips the weights out and opens the contacts.
If you're confident in your ability, pull the motor off, clean it out good, check the bearings, and clean and lightly lube the centrifugal mechanism.