Particles P and Q have masses 0.4\,\text{kg} and m\,\text{kg} respectively. P is connected to the fixed point A by a light inextensible string of length 0.5\,\text{m}, which makes an angle of 60^\circ with the vertical. P and Q are linked by a light inextensible vertical string. Q is connected to the fixed point B, vertically below A, by a light inextensible string. BQ is taut and horizontal. The particles move in horizontal circles about an axis through A and B with constant angular speed \omega\,\text{rad s}^{-1} (see diagram). The tension in the string between P and Q is 1.5\,\text{N}.
(i)[4]
Find the tension in AP, and determine the value of \omega.
(ii)[3]
Find m together with the tension in BQ.
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