4 A particle, of mass 0.8 kg , is attached to one end of a light inextensible string. The other end of the string is attached to the fixed point \(O\). The particle is set in motion, so that it moves in a horizontal circle at constant speed, with the string at an angle of \(35 ^ { \circ }\) to the vertical. The centre of this circle is vertically below \(O\), as shown in the diagram.
\includegraphics[max width=\textwidth, alt={}, center]{8ca9234e-1a01-4e35-8b1b-17c6039cf8d7-08_808_600_520_721} The particle moves in a horizontal circle and completes 20 revolutions each minute.

1. Find the angular speed of the particle in radians per second.
2. Find the tension in the string.
3. Find the radius of the horizontal circle.