You could check the pump for a tag, and if one exists, go to the manufacturer's site for technical data on the pump, which would probably include the motor size that is intended for it. Then, by comparing the RPM that it is intended to run at with the pitch ratio between the pump and motor pulleys, determine what RPM is needed. With the horsepower, RPM, and physical measurements of the motor, which would give you the frame size, you could get a new motor. Honestly though, with a tank that looks that marginal, and the general appearance of the compressor, which would cause me to question the integrity of the valves and other key components, I would put the money for a new motor, along with whatever scrap value the rest of it has, toward a new unit from TSC or other vendor. Not being critical of your air compressor, but just saying that it appears that the motor could be just the first step in a series of purchases to get it running properly.