Problem $2.$ The three small rods, each of mass $\backslash ($ m $\backslash )$ and length $\backslash ($ I $\backslash ),$ are rigidly mounted at their centers to the shaft, which rotates with the angular velocity $\backslash (\backslash$omega $\backslash )$ as shown. The axes of the rods are in the $\backslash ($ x$,$ y$,$ a n d z $\backslash )$ directions, respectively, and their diameters are negligible compared with the other dimensions. Determine the total angular momentum $\backslash (\backslash$mathbf$\{$H$\}\backslash )$ of the three rods with respect to the coordinate origin O $,$ as follows: $($a$)$ The component $\backslash (\backslash$mathrm$\{$H$\}\_\{\backslash$mathrm$\{$x$\}\}\backslash ),($b$)$ the component $\backslash (\backslash$mathrm$\{$H$\}\_\{\backslash$mathrm$\{$y$\}\}\backslash ),($c$)$ the component $\backslash (\backslash$mathrm$\{$H$\}\_\{\backslash$mathrm$\{$z$\}\}\backslash ).$