Galactic angular velocity of interstellar cloud

AI Thread Summary
The discussion centers on the relationship between the Galactic angular velocity (Ω) of an interstellar cloud and its ability to collapse radially. It is established that if Ω exceeds the threshold of sqrt(4πGρ/3), the cloud cannot collapse, highlighting the stabilizing effect of higher angular velocities. Participants are encouraged to conceptualize why increased angular velocity prevents collapse, considering extreme cases. The conversation also explores the conditions necessary for the cloud to achieve equilibrium, noting that collapse occurs at zero angular velocity and is inhibited at high velocities. Understanding these dynamics is crucial for analyzing the stability of interstellar clouds in the Galactic context.
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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.
 
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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).
 

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