  Shear viscosity becomes anisotropic in a rotating medium. It is discovered
here that for rotating thermalized quantum systems such as those created in
relativistic heavy-ion collisions, the coeffficient of shear viscosity breaks
up into five independent components. Similar phenomena were also discovered for
quark-gluon plasma in the presence of the magnetic field. Like the Lorentz
force at a finite magnetic field, the Coriolis force also creates anisotropic
viscosity at nonzero rotation. As a first approach, for simplicity, the
calculations are done in the nonrelativistic prescription, with a future
proposal to extend it toward a relativistic description. Introducing the
Coriolis force term in relaxation time approximated Boltzmann transport
equation, we have found different effective relaxation times along the
parallel, perpendicular, and Hall directions in terms of actual relaxation time
and rotating time period. Comparing the present formalism with the finite
magnetic field picture, we have shown the equivalence of roles between the
rotating and cyclotron time periods, where the rotating time period is inverse
of twice the angular velocity.
