$17\mathrm{.}82$ A $3-$kg rod of length $800$ mm can slide freely in the $240-mm$ cylinder $DE,$ which in turn can rotate freely in a horizontal plane. In the position shown, the assembly is rotating with an angular velocity of magnitude $=40ra\frac{d}{s}$ and end $B$ of the rod is moving toward the cylinder at a speed of $75m\frac{m}{s}$ relative to the cylinder. Knowing that the centroidal mass moment of inertia of the cylinder about a vertical axis is $0\mathrm{.}025kg*m^2$ and neglecting the effect of friction, determine the angular velocity of the assembly as end $B$ of the rod strikes end $E$ of the cylinder.