The two $2-$kg gears $\backslash ($ A $\backslash )$ and $\backslash ($ B $\backslash )$ are attached to the ends of a $\backslash (5-\backslash$mathrm$\{$kg$\}\backslash )$ slender bar. The gears roll within the fixed ring gear $\backslash ($ C $\backslash ),$ which lies in the horizontal plane. $($Figure $1)$

Part A

If a $\backslash (10-\backslash$mathrm$\{$N$\}\backslash$cdot $\backslash$mathrm$\{$m$\}\backslash )$ torque is applied to the center of the bar as shown, determine the number of revolutions the bar must rotate starting from rest in order for it to have an angular velocity of $\backslash (\backslash$omega$\_\{$A B$\}=19\backslash$mathrm$\{$rad$\}/\backslash$mathrm$\{$s$\}\backslash ).$ For the calculation, assume the gears can be approximated by thin disks.

Express your answer using three significant figures.

View Available Hint$($s$)$

the number of revolutions $\backslash (=\backslash )$

Previous Answers

Incorrect; Try Again; $5$ attempts remaining Figure

$1$ of $1$