  Observations show that (i) multiple gas phases can coexist in the atmospheres
of galaxies and clusters; (ii) these atmospheres may be significantly rotating
in the inner parts, with typical velocities that approach or even exceed the
local sound speed. The thermal instability is a natural candidate to explain
the formation of cold structures via condensation of a hotter gas phase. Here
we systematically study the effect of rotation on the thermal stability of
stratified plane-parallel atmospheres, using both analytical arguments and
numerical simulations. We find that the formation of cold structures starting
from small isobaric perturbations is enhanced in the regions where the rotation
of the system is dynamically important (i.e. when the rotational velocity
becomes comparable to the sound speed). In particular, the threshold value of
the ratio between the cooling and dynamical time $t_{\rm cool}/t_{\rm dyn}$
below which condensations can form is increased by a factor up to $\sim 10$ in
the presence of significant rotation. We briefly discuss the implications of
our results for galaxies and clusters.
