Particles A $($mA$=10\mathrm{.}6$ kg$)$ and B $($mB$=11\mathrm{.}2$ kg$),$ initially at rest, are fixed to a rigid massless rod pin$-$connected to fixed point O $($OB$=1$m$,$AB$=0\mathrm{.}6$m$).$ Neglect the sizes of the particles.

If particle C $($mC$=1\mathrm{.}5$ kg$)$ has rightward velocity vC$=21$ m$/$s just before impact with A and sticks to A after impact, find the maximum angle to which the system rotates before temporarily achieving rest.