  We use the holographic approach to compare the Hall viscosity $\eta_H$ and
the angular momentum density ${\cal J}$ in gapless systems in $2+1$ dimensions
at finite temperature. We start with a conformal fixed point and turn on a
perturbation which breaks the parity and time reversal symmetries via gauge and
gravitational Chern-Simons couplings in the bulk. While the ratio of $\eta_H$
and ${\cal J}$ shows some universal properties when the perturbation is
slightly relevant, we find that the two quantities behave differently in
general. In particular, $\eta_H$ depends only on infrared physics, while ${\cal
J}$ receives contributions from degrees of freedom at all scales.
