Two children, A and $B,$ each weighing $30$ kg $,$ are sitting on the edge of a carousel that rotates at $(s)=2ra\frac{d}{s}.$ The mass of the carousel excluding the child is $180$ kg and has a radius $k$;$=0\mathrm{.}6m.$ If child A jumps horizontally in the direction $-$ n with respect to the carousel at a speed of $2\frac{m}{s},$ find the angular velocity of the carousel. If child B then jumps horizontally in the direction $+1$ with respect to the carousel at a speed of $2\frac{m}{s},$ what is the angular velocity of the carousel? Neglect the friction and the size of the children.