6 A uniform circular disc, of mass \(m\) and radius \(a\), has centre \(C\). The disc can rotate freely in a vertical plane about a fixed horizontal axis through the point \(A\) on the disc, where \(C A = \frac { 1 } { 2 } a\). The disc is released from rest in the position with \(C A\) horizontal. When the disc has rotated through an angle \(\theta\),

1. show that the angular acceleration of the disc is \(\frac { 2 g \cos \theta } { 3 a }\),
2. find the angular speed of the disc,
3. find the components, parallel and perpendicular to \(C A\), of the force acting on the disc at the axis.