The satellite has a mass of $200 \mathrm{~kg}$ and a radius of gyration about $z$ axis of $k_{z}=0.1 \mathrm{~m}$, excluding the two solar panels $A$ and $B .$ Each solar panel has a mass of $15 \mathrm{~kg}$ and can be approximated as a thin plate. If the satellite is originally spinning about the $z$ axis at a constant rate $\omega_{z}=0.5 \mathrm{rad} / \mathrm{s}$ when $\theta=90^{\circ}$, determine the rate of spin if both panels are raised and reach the upward position, $\theta=0^{\circ}$, at the same instant.