$1934.$ Two children

$$

and

$$

$,$ each having a mass of $30$ kg$,$ sit at the edge of the merry$-$go$-$round which is rotating at

$$

$=$

$2$

$$

rad

$/$

s

$.$

Excluding the children, the merry$-$go$-$round has a mass of $180$ kg and a radius of gyration

$$

$$

$=$

$0\mathrm{.}6$

$$

m

$.$

Determine the angular velocity of the merry$-$go$-$round if

$$

jumps off horizontally in the $$

$$

direction with a speed of

$2$

$$

m

$/$

s

$,$

measured with respect to the merry$-$go$-$round. What is the merry$-$go$-$round$$s angular velocity if

$$

then jumps off horizontally in the $+$t direction with a speed of

$2$

$$

m

$/$

s

$,$

measured with respect to the merry$-$go$-$round? Neglect friction and the size of each child.