A centifugal switch is a set of fly wieghts that actuate a set of electrical contacts.These contacts are normally closed and feed power from the start capacitor to the start whinding which starts the motor over.Once the motor is up to speed the flywieghts flip out and the circiut to the start whinding is broken.
The switch should be located inside the motor case behind the back(opposite the shaft end)endbell of the motor.
You can use WD-40 to get the switch frred up and then use something like silicon spray lube for permanant lube.
While you have it apart look at the contacts,they maybe dirty or burnt,if they are clean them using a fine file such as a flat needle or points file.
If it is not the switch or contacts that are the problem,then check the start capacitor,if that is not the problem then the start whinding is burnt and it is time for a new motor or a re-whind.
Use caution when handling or working on the centrifugal switch,they are many times made from bakalite or similar plastic and maybe very brittle.Also Graingers carries relacements to fit serveral different types motors.
I just need one more tool,just one!