6.

\begin{figure}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{Figure 1}
  \includegraphics[alt={},max width=\textwidth]{9e3d76a7-b997-4e46-a5dd-aeeaa5abfa4e-02_211_611_388_1845}
\end{center}
\end{figure}

A rough uniform rod, of mass $m$ and length $4 a$, is rod is held on a rough horizontal table. The rod is perpendicular to the edge of the table and a length $3 a$ projects horizontally over the edge, as shown in Fig. 1.
\begin{enumerate}[label=(\alph*)]
\item Show that the moment of inertia of the rod about the edge of the table is $\frac { 7 } { 3 } m a ^ { 2 }$.

The rod is released from rest and rotates about the edge of the table. When the rod has turned through an angle $\theta$, its angular speed is $\dot { \theta }$. Assuming that the rod has not started to slip,
\item show that $\dot { \theta } ^ { 2 } = \frac { 6 g \sin \theta } { 7 a }$,
\item find the angular acceleration of the rod,
\item find the normal reaction of the table on the rod.

The coefficient of friction between the rod and the edge of the table is $\mu$.
\item Show that the rod starts to slip when $\tan \theta = \frac { 4 } { 13 } \mu$
\end{enumerate}

\hfill \mbox{\textit{Edexcel M5  Q6 [17]}}