Engine

To be accurate, the crankshaft has to be rotating if the engine is running. It is an integral part of the process. What you're seeing is not the crankshaft. Rather, there is a harmonic balancer, (aka "vibration damper") bolted to the snout of the crankshaft. That has a center hub, and a cast iron ring glued to it.

For many decades a pulley was bolted to the center hub of the vibration damper to run the belts. On your engine, that outer ring is the pulley. That means all the stress on the pulley from driving the power accessories is tugging on the glue holding the outer ring to the hub. It is not uncommon for that glue to let go.

There are three things to look at to see why the belt is not moving. First, with the engine running, see if that center hub is rotating. If it is not, it can be as simple as the large bolt in the center came loose, but more commonly the hub broke and is not being turned by the crankshaft. Next, if the hub is turning, see if the outer ring is turning. If you cannot safely get in there to see it, put a chalk mark or piece of tape on the hub and on the ring, next to each other. If the outer ring is slipping, the chalk lines will no longer be lined up after running the engine for a few seconds. Third, if that outer ring is rotating, the belt is broken or loose. Serpentine belts seem to not break real often. It is more common to find a weak or broken spring-loaded tension-er pulley. To check for that, (please do this with the engine not running!), Tug on the belt at a convenient spot, then observe if it gets pulled back tight when you let go of it. Most people can tug on it with one hand, but it should pull pretty hard.