Do you have all disc brakes or do you have drum brakes? If you have disc brakes, you could have a loose shield. You could also have worn out pads, which would allow metal-to-metal contact.
If you have drum brakes, it could be that a piece of lining has broken loose, and gets caught up in one direction, or something kind of like that. If you have missing lining on the rear shoe, it will make the most noise when the car is moving in the reverse direction. It could also be that you have a broken retracting spring, and one of the shoes digs in when the wheels spin in the appropriate direction (if rear upper shoe retracting spring broke, shoe would normally trail on the drum when vehicle was moving forward, but would dig into drum when drum spun in reverse, though this would tend to do so even when brakes weren't applied, and unless you had metal-to-metal contact, you probably wouldn't hear a grinding sound).
Inspect brakes. Definitely a good idea no matter what the problem is. It sounds most likely like a brake problem. Check the wheels and axles for looseness, though this would tend to make noise in any direction, and not necessarily a grinding one.
Tuesday, September 18th, 2007 AT 12:51 PM