  Stability analyses for equilibria of the compressible reduced
magnetohydrodynamics (CRMHD) model are carried out by means of the
Energy-Casimir (EC) method. Stability results are compared with those obtained
for ideal magnetohydrodynamics (MHD) from the classical {\delta}W criterion. An
identification of the terms in the second variation of the free energy
functional for CRMHD with those of {\delta}W is made: two destabilizing effects
present for CRMHD turn out to correspond to the kink and interchange
instabilities in usual MHD, while the stabilizing roles of field line bending
and compressibility are also identified in the reduced model. Also, using the
EC method, stability conditions in the presence of toroidal flow are obtained.
A formal analogy between CRMHD and a reduced incompressible model for
magnetized rotating disks, due to Julien and Knobloch [EAS Pub. Series, 21, 81
(2006)], is discovered. In light of this analogy, energy stability analysis
shows that the condition for magnetorotational instability (MRI) for the latter
model, corresponds to the condition for interchange instability in CRMHD, with
the Coriolis term and shear velocity playing the roles of the curvature term
and pressure gradient, respectively. Using the EC method, stability conditions
for the rotating disk model, for a large class of equilibria with possible
non-uniform magnetic fields, are obtained. In particular, this shows it is
possible for the MRI system to undergo, in addition to the MRI, another
instability that is analogous to the kink instability. For vanishing magnetic
field, the Rayleigh hydrodynamical stability condition is recovered.
