6. A uniform circular disc, of radius \(r\) and mass \(m\), is free to rotate in a vertical plane about a fixed smooth horizontal axis \(L\) which is perpendicular to the plane of the disc and passes through a point which is \(\frac { 1 } { 4 } r\) from the centre of the disc. The disc is held at rest with its centre vertically above the axis. The disc is then slightly disturbed from its rest position. You may assume without proof that the moment of inertia of the disc about \(L\) is \(\frac { 9 m r ^ { 2 } } { 16 }\).

1. Show that the angular speed of the disc when it has turned through \(\frac { \pi } { 2 }\) is \(\sqrt { } \left( \frac { 8 g } { 9 r } \right)\).
2. Find the magnitude of the force exerted on the disc by the axis when the disc has turned through \(\frac { \pi } { 2 }\).