In the figure below, three thin rods are all connected at their centers. The rods each have the same length $\backslash ($ L $\backslash )$ and mass $\backslash ($ m $\backslash ),$ and they are all perpendicular to one another. Each rod lies on one of the $\backslash ($ x $\backslash ),\backslash ($ y $\backslash ),$ or $\backslash ($ z $\backslash )-$axes as shown. The entire structure formed by the rods is rotated about an axis that is parallel to the $\backslash ($ y $\backslash )-$axis and passes through the end of the rod that lies on the $\backslash ($ x $\backslash )-$axis. What is the moment of inertia of this structure about the axis of rotation? $($Use any variable or symbol stated above as necessary.$)$

$\backslash [$

I$=$

$\backslash ]$

Consider the moment of inertia for each individual rod. For the rod on the $\backslash ($ x $\backslash )-$axis, what is the formula for the moment of inertia when the axis is at one end of the rod? For the rod on the $\backslash ($ z $\backslash )-$axis, consider the moment of inertia if the axis were at the center$-$can you then apply the parallel axis theorem? For the rod on the $\backslash ($ y $\backslash )-$axis, note that each point of the rod is the same distance away from the axis of rotation. How can you find the moment of inertia of each point?