### A.4 Angular momentum balance

An equation for the conservation of angular momentum in the anelastic system can be obtained by
averaging the zonal component of Equation (40) over longitude and multiplying by the moment arm,
. The result is:
where
As in the remainder of the paper, angular brackets denote longitudinal averages and the subscript
denotes the meridional components, e.g., . Note that the net contribution
from the magnetic terms and depends only on the magnetic tension, since the
longitudinal magnetic pressure gradients (both fluctuating and mean) vanish when integrated over
.