Galactic angular velocity of interstellar cloud

[bmace]

I've got a question that I am stumped on right now

Show that if the Galactic angular velocity $$\Omega$$
of an interstellar cloud is > sqrt(4piG$$\rho$$/3), the cloud can not collapse in the radial direction. Estimate $$\Omega$$ and compare it to the rotation rate of the Galaxy.

 

[zhermes]

What is stumping you?
Start out conceptually, why would a higher angular velocity prevent a cloud from collapsing?---It might help to think about extremal cases.

Under what conditions would the cloud be in equilibrium?---I.e. if it collapses at zero angular velocity, and won't collapse at very high velocities... where will it be in equilibrium (in the radial direction).