Show that the moment of inertia of the body about \(L\) is \(\frac { 77 m a ^ { 2 } } { 4 }\).
When \(P R\) is vertical, the body has angular speed \(\omega\) and the centre of the disc strikes a stationary particle of mass \(\frac { 1 } { 2 } \mathrm {~m}\). Given that the particle adheres to the centre of the disc,
find, in terms of \(\omega\), the angular speed of the body immediately after the impact.