If I have a charge being conducted through a rotating superconductor, is there a rotational speed at which that charge is actually static?
Try it. Faraday would set it up and see what happened. Sometimes there are surprises.
Not according to Einstein's theory of relatively. Light- electromagnetism always moves at a constant speed. No object can "catch up" to a photon and hold it.
That's where things get weird. Our conceptions of 3 dimensional space are a reliable construct in a slow moving world. When velocities increase space and time change, e.g. time dilation and the Lorentz contraction.
At high speed we live in a sci fi universe.