A Simple Demonstration of Space/Time Relativity

[Vince]

As others have said when things are spinning the speed is measured in radians/sec not a distance per second.  So all points on the disk have the same radial speed.  As the points go further out from the center they have to travel a longer distance to keep up but they are still going the same radians/second (radial speed) as every other point.

And is there no connection between radial speed and time dilation?

sure. There is a time dilation between any objects moving at different velocities. However at slow speeds the dilation is so small it is not noticed. Time on the ISS is lagging behind the earths about 0.007 seconds every year I think.