A motor will spin fine on 50 or 60hz. The motor itself isn't likely any different, just the diameter up top where the idler or turret or whatever runs against it. It will spin too fast on 60hz, but it will certainly spin. Small possibility there is a little extra iron in the core of a 50hz motor to keep it from saturating, but if anything that will just make it run slightly cooler.
Anyway, if it doesn't spin freely by hand, I'd start there. If this is a somewhat typical small open frame motor you can take the screws out of it and split it in 3 pieces. Should have two end bells with the bearings, the rotor (the part that doesn't spin) and the stator (the part that does). The stator may or may not slide out of the upper end, depending what its got up top. Pulley with a screw might let it come off, but it may be shrink fit to the shaft in which case its just coming along for the ride.
either way, clean the bearings in the end bells. Wipe the ends of the motor shaft with solvent, take a Q tip with a smidge of mineral sprits and lightly swap out the bearing itself if you can. Put some sewing machine oil in the felt around the bearing, and a few drops on the motor shaft. Put it back together and make sure it spins. If its sticky, maybe lightly whack the frame of the motor with a screwdriver handle to re-align everything. The bearings are generally a sleeve type that look like a bronze marble with a hole drilled through them. They will rotate in their pockets with a little bit of percussion and the shaft should spin nicely once they do.
If you happen to know someone with a lathe, they can make this into a 60hz motor. Basically the diameter up top needs to be made 20% smaller. Not hard to do, just needs to be done very accurately or the speed won't be proper.