$17\mathrm{.}74$ The $\backslash (60-\backslash$mathrm$\{$lb$\}\backslash )$ uniform disk $\backslash ($ A $\backslash )$ and the bar $\backslash ($ B C $\backslash )$ are at rest and the $10-$lb uniform disk $\backslash ($ D $\backslash )$ has an initial angular velocity $\backslash (\backslash$boldsymbol$\{\backslash$omega$\}\_\{1\}\backslash )$ of magnitude $440$ rpm when the compressed spring is released and disk $\backslash ($ D $\backslash )$ contacts disk $\backslash ($ A $\backslash ).$ The sistem rotates freely about the vertical spindle $\backslash ($ B E $\backslash ).$ After a period of slippage. disk $\backslash ($ D $\backslash )$ rolls without slipping. Knowing that the magnitude of the final angular velocity of disk $\backslash ($ D $\backslash )$ is $176$ rpm $,$ determine the final angular velocities of bar $\backslash ($ B C $\backslash )$ and disk $\backslash ($ A $\backslash ).$ Neglect the mass of bar $\backslash ($ B C $\backslash ).$