Problem $16\mathrm{.}38$ modifled

The $25\mathrm{.}0-1$bf double pulley shown is at rest and in equilibrium when a constant $3\mathrm{.}7$ lbf $-$ ft couple $M$ is applied. The radius of gyration of the double pulley is $6\mathrm{.}0$ in $.$ Neglecting the effect of friction.

Determine the angular acceleration of the double pulley.

$=$ rad$/$s $($:${?}^2$