  In a granular gas of rough particles the axis of rotation is shown to be
correlated with the translational velocity of the particles. The average
relative orientation of angular and linear velocities depends on the parameters
which characterise the dissipative nature of the collision. We derive a simple
theory for these correlations and validate it with numerical simulations for a
wide range of coefficients of normal and tangential restitution. The limit of
smooth spheres is shown to be singular: even an arbitrarily small roughness of
the particles gives rise to orientational correlations.
