HW$12\mathrm{.}5.$ Bar impacts support

Just before a small massless peg A embedded in the $9\mathrm{.}2-$kgl$=1\mathrm{.}9$m O$,$ the bar has the position shown, angular velocity $\backslash$omega $=0\mathrm{.}25$ra$($d$)/($s$)($CW$)$ and v$\_($G$)=1($m$)/($s$)$

$($downward$).$ A is located a distance x$=0\mathrm{.}32$m from the left end of the bar. After impact, A remains at O and

the bar rotates about this fixed point.

Compute a$\backslash$omega $\_(2),$ the magnitude of the bar's angular velocity just after impact and b$\backslash$omega $\_(3),$ the magnitude of the

bar's angular velocity at the instant that it has rotated $30$ degrees clockwise after the impact. g$=9\mathrm{.}81($m$)/($s$^(2)).$

$($Assume the bar does not contact the ground.$)$

ANSWERS: $\backslash$omega $2=1\mathrm{.}01071326199($rad$)/($s$),\backslash$omega $3=3\mathrm{.}14312317858($rad$)/($s$).$

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