Summarize this article:

Many electric motor failures are caused by bearing failures.  The bearings allow the shaft or rotor assembly to turn freely and smoothly in the frame.  Bearings are located at both ends of the motor which are sometimes called "bell housings" or "end bells". There are several types of bearings used.  Two popular types are brass sleeve bearings and steel ball bearings.  Many have fittings for lubrication while others are permanently lubricated or "maintenance free". To perform a cursory check of the bearings, place the motor on a solid surface and place one hand on the top of the motor, spin the shaft/rotor with the other hand. Closely watch, feel, and listen for any indication of rubbing, scraping, or unevenness of the spinning rotor. The rotor should spin quietly, freely and evenly. A small amount of movement in and out (most household fractional horsepower types should be less than 1/8" or so) is permitted, but the closer to "none" the better. A motor that has bearing-related issues when run will be loud, overheat the bearings, and potentially fail catastrophically.

Summary:
Begin to check the bearings of the motor. Perform a check of the bearings. Next, push and pull the shaft in and out of the frame.