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A $9-$kg uniform disk is attached to the $5-$kg slender rod $\backslash ($ A B $\backslash )$ by means of frictionless pins at $\backslash ($ B $\backslash )$ and $\backslash ($ C $\backslash ).$ The assembly rotates in a vertical plane under the combined effect of gravity and of a couple $\backslash (\backslash$mathbf$\{$M$\}\backslash )$ which is applied to rod $\backslash ($ A B $\backslash ).$ At the instant shown, the assembly has an angular velocity of $\backslash (6\backslash$mathrm$\{$rad$\}/\backslash$mathrm$\{$s$\}\backslash )$ and an angular acceleration of $\backslash (31\backslash$mathrm$\{$rad$\}/\backslash$mathrm$\{$s$\}^\{2\}\backslash ),$ both counterclockwise.

Determine the couple $\backslash (\backslash$mathbf$\{$M$\}\backslash ).$

The couple $\backslash (\backslash$mathbf$\{$M$\}\backslash )$ is N$-$m $\backslash (\backslash$circlearrowleft $\backslash )$