$1.$ A cable is wrapped around the inner diameter of the double wheel as shown. The cable is pulled horizontally at a speed of $\backslash (12\backslash$mathrm$\{$ft$\}/\backslash$mathrm$\{$s$\}\backslash ),$ turning the double wheel, which rolls on its inner diameter surface without slipping.

a$.$ Determine the angular velocity $\backslash (\backslash$omega $\backslash )$ of the wheel, in rad$/$s$.$

b$.$ Determine the magnitude and direction of the velocities of points A $,$ D $,$ and E at the instant shown, in $\backslash (\backslash$mathrm$\{$ft$\}/\backslash$mathrm$\{$s$\}\backslash ).$