  The specific shear viscosity $\bar\eta$ of a classically rotating system of
nucleons that interact via a monopole pairing interaction is calculated
including the effects of thermal fluctuations and coupling to pair vibrations
within the selfconsistent quasiparticle random-phase approximation. It is found
that $\bar\eta$ increases with angular momentum $M$ at a given temperature $T$.
In medium and heavy systems, $\bar\eta$ decreases with increasing $T$ at
$T\geq$ 2 MeV and this feature is not affected much by angular momentum. But in
lighter systems (with the mass number $A\leq$ 20), $\bar\eta$ increases with
$T$ at a value of $M$ close to the maximal value $M_{max}$, which is defined as
the limiting angular momentum for each system. The values of $\bar\eta$
obtained within the schematic model as well as for systems with realistic
single-particle energies are always larger than the universal lower-bound
conjecture $\hbar/(4\pi k_B)$ up to $T$=5 MeV.
