4. A uniform circular disc, of mass \(2 m\) and radius \(a\), is free to rotate in a vertical plane about a fixed, smooth horizontal axis through a point of its circumference. The axis is perpendicular to the plane of the disc. The disc hangs in equilibrium. A particle \(P\) of mass \(m\) is moving horizontally in the same plane as the disc with speed \(\sqrt { } ( 20 \mathrm { ag } )\). The particle strikes, and adheres to, the disc at one end of its horizontal diameter.

1. Find the angular speed of the disc immediately after \(P\) strikes it.
2. Verify that the disc will turn through an angle of \(90 ^ { \circ }\) before first coming to instantaneous rest.