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I have a 1981 Corvette with AT transmission. I was out driving it yesterday and was at a stop light and started to accelerate when the light turned green. It felt like the back right tire of the car started wobbling, as if the tire was not on the lugs good. I pulled over and the tire was attached just fine and looked to be straight on.
I'm not a suspension guy, so I'm assuming it is the u joints perhaps on the half shafts going bad? I drove it home slowly .. parked it in the garage. I did jack it up and tried to see if there was any movement, but no significant movement of the U Joints that I could tell.
First thing that comes to mind is a wheel bearing when you mention "wobble." When my trailing arm bushings started getting bad, I got a "sway" when I got in the gas and the gentleman above may very well be correct with his call. I'm sure one of the guys more knowledgeable than I can set you straight. Best of luck.
You might also check to see if your shims are still in place. If they are missing or the bushing is loose on the bolt the outcome can easily fit the description of what you have experienced.
Check out the Trailing Arm Bushing Kit in the image below. This is what you are looking for to see if there is any lateral movement about the Trailing Arm Bolt.
I had the same thing on my 71. Driver side rear wheel wobbled when going down the road. Bearing made no noise. Rebuilt the trailing arms and wobble is now gone.
81 Corvette back wheel wobble
