Required information

Gear $\backslash ($ A $\backslash )$ weighs $4\mathrm{.}000$ lb and has a radius of gyration of $1\mathrm{.}3$ in ; Gear $\backslash ($ B $\backslash )$ weighs $9\mathrm{.}000$ lb and has a radius of gyration of $3$ in $.$; gear $\backslash ($ C $\backslash )$ weighs $12\mathrm{.}00$ lb and has a radius of gyration of $4\mathrm{.}3$ in $.$ A couple $\backslash (\backslash$mathbf$\{$M$\}\backslash )$ of constant magnitude of $40$ lb $-$in is applied to gear $\backslash ($ A $\backslash ).$

Determine the angular acceleration of gear C $.$