Meriam, Kraige & Bolton — Introduction to Three-Dimensional Dynamics of Rigid Bodies: Problem 7_48

7/48 The spheres of Prob. 7/47 are replaced by three rods, each of mass $m$ and length $l$, mounted at their centers to the shaft, which rotates with the angular velocity $\omega$ as shown. The axes of the rods are, respectively, in the $x$-, $y$-, and $z$-directions, and their diameters are negligible compared with the other dimensions. Determine the angular momentum $\mathbf{H}_O$ of the three rods with respect to the coordinate origin $O$.