Problem source

\textit{In this question, all gravitational forces are to be neglected. }

A rigid frame is constructed from 12 equal uniform rods, each of length
$a$ and mass $m,$ forming the edges of a cube. Three of the edges
are $OA,OB$ and $OC,$ and the vertices opposite $O,A,B$ and $C$
are $O',A',B'$ and $C'$ respectively. Forces act along the lines
as follows, in the directions indicated by the order of the letters:
\begin{alignat*}{3}
2mg\mbox{ along }OA, & \qquad & mg\mbox{ along }AC', & \qquad & \sqrt{2}mg\mbox{ along }O'A,\\
\sqrt{2}mg\mbox{ along }OA', &  & 2mg\mbox{ along }C'B, &  & mg\mbox{ along }A'C.
\end{alignat*}
\begin{questionparts}
\item The frame is freely pivoted at $O$. Show that the direction of the line
about which it will start to rotate is
$\begin{pmatrix}1\\
1\\
2
\end{pmatrix}$ with respect to axes
along $OA$, $OB$ and $OC$ respectively.
\item Show that the moment of inertia of the rod 
$OA$ about the axis $OO'$ is $2ma^2/9$ and about a parallel axis through
 its mid-point is $ma^2/18$. Hence find the 
moment of inertia of $B'C$ about $OO'$ and show that the moment of inertia
of the frame about $OO'$ is $14ma^2/3$.  If the frame
 is freely pivoted about the line $OO'$ and the forces continue 
to act along the specified lines, find the initial angular 
acceleration of the frame.   
\end{questionparts}