Problem $16\mathrm{.}124-$ Reaction at one end of a uniform rod fitted with a small wheel

The $4-$kg uniform rod $\backslash ($ A B D $\backslash )$ is attached to the crank $\backslash ($ B C $\backslash )$ and is fitted with a small wheel that can roll without friction along a vertical slot. Knowing that at the instant shown crank $\backslash ($ B C $\backslash )$ rotates with an angular velocity of $\backslash (12\backslash$mathrm$\{$rad$\}/\backslash$mathrm$\{$s$\}\backslash )$ clockwise and an angular acceleration of $\backslash (15\backslash$mathrm$\{$rad$\}/\backslash$mathrm$\{$s$\}^\{2\}\backslash )$ counterclockwise, determine the reaction at $\backslash ($ A $\backslash ).$