2004 F150 4.6L XLT 2WD
 

I'm repairing a truck that was hit pretty hard in the back. I noticed what seems to be a lot of rotation in the rear wheels when in park (back end off ground). I can move a wheel about half a rotation. I'm trying to decide if I have a differential problem or a transmission problem... or maybe it's not a problem! I don't hear any whining ,grinding, or bumping noises while driving. The truck has a lot of miles (almost 200K). Any ideas or tests that I can try to determine if everything is safe?

I do hear a slight double bump when accelerating normally from a stop. We removed the drive shaft and cleaned up and re-greased the splines. Noise still present. in looking at the leaf spring bushings, it appears the passenger side bushing is badly worn. Going to replace both sides in the back.