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A non-uniform rectangular lamina $A B C D$ has mass 6 kg . The centre of mass $G$ of the lamina is 0.8 m from the side $A D$ and 0.5 m from the side $A B$ (see diagram). The moment of inertia of the lamina about $A D$ is $6.2 \mathrm {~kg} \mathrm {~m} ^ { 2 }$ and the moment of inertia of the lamina about $A B$ is $2.8 \mathrm {~kg} \mathrm {~m} ^ { 2 }$.

The lamina rotates in a vertical plane about a fixed horizontal axis which passes through $A$ and is perpendicular to the lamina.\\
(i) Write down the moment of inertia of the lamina about this axis.

The lamina is released from rest in the position where $A B$ and $D C$ are horizontal and $D C$ is above $A B$. A frictional couple of constant moment opposes the motion. When $A B$ is first vertical, the angular speed of the lamina is $2.4 \mathrm { rad } \mathrm { s } ^ { - 1 }$.\\
(ii) Find the moment of the frictional couple.\\
(iii) Find the angular acceleration of the lamina immediately after it is released.

\hfill \mbox{\textit{OCR M4 2007 Q3 [9]}}