Answer
The maximum RPM for an external ring is limited by centrifugal force, which causes the ring to expand radially. The speed $N$ at which the ring begins to lift off the groove is given by $N = _x000c_rac{1}{ ext{rad/sec conversion}} imes _x000c_rac{1}{D_m} imes _x000c_rac{ ext{Groove Depth}}{ ext{Expansion Constant}}$. More formally, the critical velocity $V_c$ is derived by balancing the centrifugal force $F_c = m imes _x000c_rac{v^2}{R}$ against the ring's internal elastic grip. The formula used by engineers is $V = _x000c_rac{1}{ ext{π} D_i} imes ext{sqrt} _x000c_rac{48 E I g riangle}{w _x000d_ho A R_m^4}$, where $ riangle$ is the radial clearance between the ring and the groove, $_x000d_ho$ is the density, and $I$ is the moment of inertia. Above this speed, the ring loses its 'cling' and can be ejected.
