  The total angular momentum associated with the edge mass current flowing at
the boundary in the superfluid $^3$He A-phase confined in a disk is proved to
be $L=N\hbar/2$, consisting of $L^{\rm MJ}=N\hbar$ from the Majorana
quasi-particles (QPs) and $L^{\rm cont}=-N\hbar/2$ from the continuum state. We
show it based on an analytic solution of the chiral order parameter for
quasi-classical Eilenberger equation. Important analytic expressions are
obtained for mass current, angular momentum, and density of states (DOS).
Notably the DOS of the Majorana QPs is exactly $N_0/2$ ($N_0$: normal state
DOS) responsible for the factor 2 difference between $L^{\rm MJ}$ and $L^{\rm
cont}$. The current decreases as $E^{-3}$ against the energy $E$, and $L(T)
\propto -T^2$. This analytic solution is fully backed up by numerically solving
the Eilenberger equation. We touch on the so-called intrinsic angular momentum
problem.
