Does T-belt turn when cranking?

I was driving home from work today when my car just died (88 2.3na A4LD). Pulled off to the side and when I tried to restart it it sounded different like like the engine was spinning more. I got out and tried to start from under the hood, the engine is spinning but the timing belt is not moving. When the engine is cranking the timing belt should spin too, right?, or am I mistaken.

I had the car towed home and that is as far as I have gotten so far. So if the belt is supposed to turn what would cause it not to? If it isn't supposed to spin on cranking then I know to start checking all the other problems it could be.

Thank you for any help.

That is what I was thinking. It didn't make sense to me that the belt wouldn't turn when cranking, what would get the valves moving and such then? This should be fun.

Thank you Red_LX. I feel dumb now but I had never worked with a belt before, just chains but I figured it had to be the same.

Turns out the belt was missing a large section of teeth and was rotted pretty bad too. It was a bit of a pain but it's all back together now and running fine thanks to all the info around for the 2.3.