  A simple variational calculation is presented showing that a uniformly
rotating barotropic fluid in an external potential attains a true energy
minimum if and only if the rotation profile is everywhere subsonic. If regions
of supersonic rotation are present, fluid variations exist that could take the
sytem to states of lower energy. In any given system, these states may or may
not be dynamically accessible, but their existence is important. It means that
extending the degrees of freedom available to the fluid (say by weak magnetic
fields) may open a path to fluid instabilities. Whether astrophysical gaseous
nebula tend toward states of uniform rotation or toward more Keplerian
core-disk systems appears to be largely a matter of whether the rotation
profile is transonic or not. The suggestion is made that the length scale
associated with coherent molecular cloud cores is related to the requirement
that the cores be stable and rotate subsonically.
