I can hear the motor running, but it does not spin

I think this is a dryer we're talking about -- First link is more of visual aid
Believe your motor is fine -- sounds like a belt problem -- check belt or tensioner

How to Replace the Motor on a Dryer (http://repair2000.com/wp_motor_repl.htm)

These two links may be helpful for anyone working on a dryer

Appliance Parts from RepairClinic.com - Detailed Appliance Illustration (http://www.repairclinic.com/0100_15.asp)

Appliance Parts from RepairClinic.com - Detailed Appliance Illustration (http://www.repairclinic.com/0100_16.asp)

Last link shows how belts install -- this may be helpful if belt is broken

Belt Installation (http://www.affordableappliance.com/Tips/TipImages/beltdiagrams.htm)