... How are you going to apply 500W of power to rotating a generator and expect the generator to be able to output more than the input 500W (theoretical 100% efficiency)

Your not directly but with the pullies you can.
You're*, pulleys*
you also seem to have forgotten the torque penalty when using a gear ratio to increase your speed. the generator needs speed AND torque. if your motor is only capable of outputting a finite amount of power. putting a pulley on it wont have any affect. you'll just bog the motor down and it'll still have the same rotational speed on the input shaft of the generator.
try again.
