A $250\mathrm{.}0$ kg playground merry$-$go$-$round has a radius of $1\mathrm{.}80$ m and, with a $36\mathrm{.}0$ kg child located at

$1\mathrm{.}30$ m from the merry$-$go$-$round$$s center, is spinning at $38\mathrm{.}0$ rad$/$s$.$