A rough horizontal disc rotates with constant angular speed \(\omega\,\text{rad s}^{-1}\). A particle \(P\) of mass \(1.6\) kg is at distance \(1.5\) m from the centre \(O\), attached to a point \(A\) vertically above \(O\) by a light elastic string. The natural length is \(2\) m, the modulus of elasticity is \(32\) N, and the coefficient of friction is \(0.5\). The particle is on the point of slipping in the direction \(OP\).

(a) Given that the tension is \(8\) N, show that \(\sin\alpha=0.6\).

(b) Find the number of revolutions per minute made by the disc and the particle.