Thanks for the quick reply. I figured that the normal formulas for rotational motion might break down, but I wasn't personally aware of cases in which they failed, so I wasn't sure. Is this one of those cases where a theory of quantum gravity would be important, or is there an existing framework...
And if so, how much? Should the radius be thought of as zero, an infinitesimal, or as the Planck length?
v2/r = ω2r
If its zero, then you immediately run into a problem when trying to calculate it with linear velocity.
v2/r = ar
v2/0 = undefined
OR
ω2r = ar
ω20 = 0
Which would mean that...