A uniform stick $1\mathrm{.}4$ mm long with a total mass of $270$ gg is pivoted at its center. A $3\mathrm{.}1-$gg bullet is shot through the stick midway between the pivot and one end The bullet approaches at $250$ m$/$sm$/$s and leaves at $140$ m$/$sm$/$s$.$ With what angular speed is the stick spinning after the collision?