Unsupported rotating ring speed limit
The maximum speed any physical thing made out of atoms can be spinned is about 3000 meters per second.
For every material made into a ring there is a maximum tangential speed it can be rotated before the forces rip it apart.
This speed depends on the materials ultimate tensile strengh (UTS).
As it turns out this speed is independent of the size of the ring.
Since in the limits of currently known physics there is an upper limit in material strengths that are reachable there is an upper limit for rotating speed.
Using one of the materials with highest known UTS (carbon nanotubes) one finds that:
This limit is at about 3000 m/s
A practical problem where the limit might matter
(TODO: add the math)
A practical problem where the limit does not apply
If infinitesimal bearings are arranged in a straight track there are no forces so the limit does not apply. So in the not so near future Interplanetary acceleration tracks may be buildable that catch spacecraft not electromagnetically but physically and that at orbital speeds.
Exceeding the limit
To exceed this rotation speed the ring would need to be supported by an enclosing non-rotating ring. Since the relative motion is about ten times thermal motion at room temperature macroscopically thick (a few millimeters) layers of infinitesimal bearing are needed that can deal with high levels of stress and deal with a bit of (reversible) strain. Even then the friction heat might be so high that these super-limit speeds can be sustained only briefly.
It is still highly unclear whether a ultra low friction levitation could be archived that would provide enough supporting force.