  A polydisperse granular gas made of inelastic and rough hard disks is
considered. Focus is laid on the kinetic-theory derivation of the partial
energy production rates and the total cooling rate as functions of the partial
densities and temperatures (both translational and rotational) and of the
parameters of the mixture (masses, diameters, moments of inertia, and mutual
coefficients of normal and tangential restitution). The results are applied to
the homogeneous cooling state of the system and the associated nonequipartition
of energy among the different components and degrees of freedom. It is found
that disks typically present a stronger rotational-translational
nonequipartition but a weaker component-component nonequipartition than
spheres. A noteworthy "mimicry" effect is unveiled, according to which a
polydisperse gas of disks having common values of the coefficient of
restitution and of the reduced moment of inertia can be made indistinguishable
from a monodisperse gas in what concerns the degree of rotational-translational
energy nonequipartition. This effect requires the mass of a disk of component
$i$ to be approximately proportional to $2\sigma_i+\langle\sigma\rangle$, where
$\sigma_i$ is the diameter of the disk and $\langle\sigma\rangle$ is the mean
diameter.
