= Homologous rotating collapse
{title2=$\Omega\propto R^{-2},\quad F_{\rm cent}/F_{\rm grav}\propto R^{-1}$}
During a spherical <stellar homology> contraction at fixed mass and <angular momentum>, a constant inertia coefficient gives $I=\alpha MR^2$ 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.
Back to article page
