A particle, \(P\), of mass \(m\) is attached to one end of a light rod of length \(L\). The other end of the rod is attached to a fixed point \(O\) so that the rod is free to rotate in a vertical plane about \(O\). The particle is held with the rod horizontal and is then projected vertically downwards with speed \(u\). The particle first comes to instantaneous rest at the point \(A\).
Explain why the acceleration of \(P\) at \(A\) is perpendicular to \(O A\).
At the instant when \(P\) is at the point \(A\) the acceleration of \(P\) is in a direction making an angle \(\theta\) with the horizontal. Given that \(u ^ { 2 } = \frac { 2 g L } { 3 }\),
find
the magnitude of the acceleration of \(P\) at the point \(A\),
the size of \(\theta\).
Find, in terms of \(m\) and \(g\), the magnitude of the tension in the rod at the instant when \(P\) is at its lowest point.