Why does my serpentine belt keep snapping on my bmw 745li 2002?

Certainly it should rotate all of the time with the belt on it, with the engine running. The power steering pump does not cycle on and off like the air conditioning compressor. The power steering pump pulley rotates by hand when not installed but may encounter resistance when installed because you will be pumping fluid through the steering system. If you have a serpentine belt, you need to check the generator pulley and the belt tension pulley, with the the belt off. They definitely rotate easily by hand. If your AC is working than the compressor pulley is turning when it cycles on and locks the outer pulley to the inner one.. You should see all of the pulleys turning with the engine running and the AC turned on and auto cycled to lock the inner pulley. You might have a pulley alignment problem if one of the above devices is lose and “floating” or wobbling.