Critical rotation of a spherical cloud
= Critical rotation of a spherical cloud
{title2=$\Omega_c^2=GM/R_c^3,\quad R_c=J^2/(\alpha^2GM^3)$}
In the spherical approximation, equatorial centrifugal acceleration balances surface gravity when $\Omega_c^2R_c=GM/R_c^2$. For $I=\alpha MR^2$ and conserved <angular momentum> $J$, this gives the displayed critical radius. Real rotating gas can deform, lose matter and exchange torques before a spherical model remains accurate at this limit.