 Homologous rotating collapse

During a spherical stellar homology contraction at fixed mass and angular momentum, a constant inertia coefficient gives $I=\alpha M{R}^2$ and solid-body rotation gives $\Omega =J/I\propto R^{-2}$. A fixed fluid label $s=r/R$ retains its enclosed mass and polar angle, so centrifugal acceleration scales as $R^{-3}$ and gravity as $R^{-2}$. Their ratio increases as $R^{-1}$. This assumes spin conservation, not continuous synchronization to an external orbit.