Part A

The operation of "reverse" for a three$-$speed automotive transmission is illustrated schematically in the figure.

$($Figure $1)$

If the crank shaft $\backslash ($ G $\backslash )$ is turning with an angular speed of $\backslash (\backslash$omega$\_\{$G$\}=35\backslash$mathrm$\{$rad$\}/\backslash$mathrm$\{$s$\}\backslash ),$ determine the angular speed of the drive shaft $\backslash ($ H $\backslash ).$ Each of the gears rotates about a fixed axis. Note that gears $\backslash ($ A $\backslash )$ and $\backslash ($ B$,$ C $\backslash )$ and $\backslash ($ D$,$ E $\backslash )$ and $\backslash ($ F $\backslash )$ are in mesh. The radii of each of these gears are reported in the figure.

Express your answer to three significant figures and include the appropriate units.