6 A particle is attached to one end of a light inextensible string. The other end of the string is attached to a fixed point \(O\). The particle is set into motion, so that it describes a horizontal circle whose centre is vertically below \(O\). The angle between the string and the vertical is \(\theta\), as shown in the diagram.
\includegraphics[max width=\textwidth, alt={}, center]{480a817d-074f-440d-829e-c8f8a9746151-6_506_442_534_794}

1. The particle completes 40 revolutions every minute. Show that the angular speed of the particle is \(\frac { 4 \pi } { 3 }\) radians per second.
2. The radius of the circle is 0.2 metres. Find, in terms of \(\pi\), the magnitude of the acceleration of the particle.
3. The mass of the particle is \(m \mathrm {~kg}\) and the tension in the string is \(T\) newtons.
   1. Draw a diagram showing the forces acting on the particle.
   2. Explain why \(T \cos \theta = m g\).
   3. Find the value of \(\theta\), giving your answer to the nearest degree.