  In recent studies, it has been discovered that phonons can carry angular
momentum, leading to a series of investigations into systems with 3-fold
rotation symmetry. However, for systems with 2-fold screw rotational symmetry,
such as $\alpha$-MoO$_3$, there has been no relevant discussion. In this paper,
we investigated the pseudoangular momentum of phonons in crystals with 2-fold
screw rotational symmetry. Taking $\alpha$-MoO$_3$ as an example, we explain
the selection rules in circularly polarized Raman experiments resulting from
pseudoangular momentum conservation, providing important guidance for
experiments. This study of pseudoangular momentum in $\alpha$-MoO$_3$ opens up
a new degree of freedom for its potential applications, expanding into new
application domains.
