$(15$ points$)$ Two particles are attached to a fixed point $($ O $)$ with rigid bars. Particle A weighs $120-$pounds and Particle B weighs $60-$pounds. Assume that the rigid bars have negligible mass, and that the system rotates on a horizontal plane. At $t=0,$ the particles have an angular velocity of $+0\mathrm{.}75$widehat$(k)[ra\frac{d}{s}].$ A clockwise moment is then applied to the system, which is defined by the following equation, where $t$ is the time in seconds.

$M_O=2t^2[lb-ft]$

When $t=1\mathrm{.}5$ seconds, determine the magnitude of the angular velocity of the particles.