How many calories burned while riding on the back of a motorcycle?

Zero.

With the exception of sweating, all you're doing in sitting on your rear.

This is wrong. If you ever rode a motorcycle you would know how tired you are after a long ride. You are always moving, watching and shifting your weight and your bike. I am not sure of the calories burned but have heard between 25 and 36 calories burned for 15 minutes of riding or 102 calories burned for an hour of riding.