Say you're five inches from the center. Then that point moves around the center at a certain speed. Now say you're four inches from the center. Then that point moves slower around the center. Three inches, two inches, one inch, it moves slower and slower. On the spindle the selected point moves slower still until you reach the exact center where at that point, the spindle isn't moving at all!
If you don't believe it, test it out. It also proves you can have a dimensionless point in physical space.
There's a certain similarity between this example and the eye of the hurricane.