$($a$)$ Calculate the total angular momentum for this two rod system about the point A$=(0,0,0)$ at the instant shown.

$($b$)$ In the presence of gravity, what is the total torque on this two rod system with respect to the point A$=(0,0,0)$ at the instant shown? A massless rod of length $\backslash (2$ d $\backslash )$ is connected to a frictionless axle rotating clockwise with angular speed $\backslash (\backslash$Omega $\backslash )$ about position A $.$ On one end of the massless rod, a distance $\backslash ($ d $\backslash )$ from the axle, is attached a mass $\backslash ($ M $\backslash ).$ On the othe of the massless rod, a distance $\backslash ($ d $\backslash )$ from the axle, is a second rod that is attached by a frictionless axle. This shorter rod has length $\backslash ($ h $\backslash ),$ mass $\backslash (2$ M $\backslash )($which is distributed uniformly across the rod$)$ and is rotating counterclock with angular speed $\backslash (\backslash$omega $\backslash ).$ The position of the rods at a single instant in time is shown in the figure below. At this instant the longer rod makes an angle $\backslash (\backslash$theta $\backslash )$ with respect to the vertical.

$($a$)$ Calculate the total angular momentum for this two rod system about the point $\backslash ($ A$=(0,0,0)\backslash )$ at the instant shown.

$($b$)$ In the presence of gravity, what is the total torque on this two rod system with respect to the point $\backslash ($ A$=(0,0,0)\backslash )$ at the instant shown?