We propose. a new model of a gas of rough hard spheres that includes i
nelastic effects. The spheres interact with each other and with the co
ntainer walls through inelastic collisions. The impulsive friction wit
hout slipping at the impacts conserves the total energy of the system,
but mixes the tangential velocity components with the angular velocit
ies of colliding spheres. We explore the - sometimes surprising - cons
equences of this in a simple billiard model.