3
\includegraphics[max width=\textwidth, alt={}, center]{181fad74-6e60-4435-a176-3edff5062c32-2_392_746_908_645} 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.

1. 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 \(2.4 \mathrm { rad } \mathrm { s } ^ { - 1 }\).
2. Find the moment of the frictional couple.
3. Find the angular acceleration of the lamina immediately after it is released.