Exercise $6\mathrm{.}11$

The thin disk is mounted on shaft $\backslash ($ A B $\backslash ),$ which coincides with a diametral line. The rotation rates $\backslash (\backslash$Omega$\_\{1\}\backslash )$ about this axis and $\backslash (\backslash$Omega$\_\{2\}\backslash )$ about the vertical are both constant. Derive expressions for the dynamic reactions at bearings $\backslash ($ A $\backslash )$ and $\backslash ($ B $\backslash ).$ It may be assumed that the bearings exert forces, but not couples, and that only the mass of the disk is significant.