A thin, uniform $3\mathrm{.}90$ kg

bar, $90\mathrm{.}0$ cm

long, has very small $2\mathrm{.}50$ kg

balls glued on at either end $($Figure $1).$ It is supported horizontally by a thin, horizontal, frictionless axle passing through its center and perpendicular to the bar. Suddenly the right$-$hand ball becomes detached and falls off, but the other ball remains glued to the bar.Find the angular velocity of the bar just as it swings through its vertical position.