$19-13.$ The smooth rod assembly shown is at rest when it is struck by a hammer at $\backslash ($ A $\backslash )$ with an impulse of $\backslash (10\backslash$mathrm$\{$~N$\}\backslash$cdot $\backslash$mathrm$\{$~s$\}\backslash ).$ Determine the angular velocity of the assembly and the magnitude of velocity of its mass center immediately after it has been struck. The rods have a mass per unit length of $\backslash (6\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$m$\}\backslash ).$