The four particles shown below are connected by rigid rods of negligible mass where $\backslash ($ y$\_\{1\}=6\mathrm{.}60\backslash$mathrm$\{$~m$\}\backslash ).$ The origin is at the center of the rectangle. The system rotates in the $\backslash ($ x y $\backslash )$ plane about the $\backslash ($ z $\backslash )$ axis with an angular speed of $\backslash (6\mathrm{.}60\backslash$mathrm$\{$rad$\}/\backslash$mathrm$\{$s$\}\backslash ).$

$($a$)$ Calculate the moment of inertia of the system about the $\backslash ($ z $\backslash )$ axis.

You can determine the moment of inertia of each particle about the $\backslash ($ z $\backslash )$ axis and then add them together. $\backslash (\backslash$mathrm$\{$kg$\}\backslash$cdot $\backslash$mathrm$\{$m$\}^\{2\}\backslash )$

$($b$)$ Calculate the rotational kinetic energy of the system.

You appear to have calculated the rotational energy correctly using your incorrect result from part $($a$).$ J