Imagine a frame A (ground) unrolling a coil at speed ~c. Imagine a second frame B (moving rectiline) following the coil and turning next to it a disk at same speed.
If both are supposed to turn at same speed, how can we have time dilation?
Rotating frame is an accelerating (non-inertial) frame! Special theory of relativity is not applicable in an accelerating (rotating) frame. Also, see this link, http://www.projects.science.uu.nl/igg/dieks/rotation.pdf
You didn't understand the thought experiment. This is not about rotating frames.
Imagine a frame A (ground) unrolling a coil at speed ~c. Imagine a second frame B (moving rectiline) following the coil (and turning next to it a disk at same speed).
Will one of the two observer (A or B) see a slower rotating disk than the coil?
I think the phrase "turning next to it a disk at same speed." is the problem. This implies the observer is rotating. Lots of problems with such a construction.