$($a$)$ A $23\mathrm{.}0-kg$ child is riding a playground merry$-$go$-$round that is rotating at $40\mathrm{.}0$ rpm $.$ What centripetal force must she exert to stay on if she is $1\mathrm{.}00$ m from its center?

$($b$)$ What centripetal force does she need to stay on an amusement park merry$-$go$-$round that rotates at $3\mathrm{.}00$ rpm if she is $5\mathrm{.}80$ m from its center?

$($c$)$ Compare each force with her weight.

force from part $($a$)=$ weight $$

$\frac{\text{f}\text{o}\text{r}\text{c}\text{e}\text{f}\text{r}\text{o}\text{m}\text{p}\text{a}\text{r}\text{t}(b)}{\text{w}\text{e}\text{i}\text{g}\text{h}\text{t}}=$