Unsupported rotating ring speed limit

 The maximum speed any physical thing made out of atoms can be spinned is about 3000 meters per second.

How natural accelerations grow with shrinking size. Offtopic: To keep waste heat from friction at practical levels it is sensible to slow down at the nanoscale that is as one goes from right to left in the diagram one moves down the lines deviating from the natural scaling law. (TODO: make a simplified graph with just the red line for this page)

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

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.

If infinitesimal bearings are arranged in a straight track there are no forces so the limit does not apply.

(TODO: add the math)

Related

• Scaling laws
• Interplanetary acceleration tracks