The specific shear viscosity $bareta$ 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 $bareta$ increases with angular momentum $M$ at a given temperature $T$. In medium and heavy systems, $bareta$ decreases with increasing $T$ at $Tgeq$ 2 MeV and this feature is not affected much by angular momentum. But in lighter systems (with the mass number $Aleq$ 20), $bareta$ 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 $bareta$ obtained within the schematic model as well as for systems with realistic single-particle energies are always larger than the universal lower-bound conjecture $hbar/(4pi k_B)$ up to $T$=5 MeV.
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