  For the affine vertex algebra $V_k(\mathfrak{g})$ at an admissible level $k$
of $\hat{\mathfrak{g}}$, we prove that certain subcategory of weak
$V_k(\mathfrak{g})$-module category is semisimple. As a consequence, we show
that $V_k(\mathfrak{g})$ is rational with respect to a family of Virasoro
elements. We also prove that certain affine vertex operator superalgebras and
minimal $W$-algebras are rational with respect to a family of Virasoro
elements.
