$($a$)$ A $15\mathrm{.}0$ kg child is riding a playground merry$-$go$-$round that is rotating at $35\mathrm{.}0$ rev $/$ min. What centripetal force $($in N$)$ must she exert to stay on if she is $1\mathrm{.}00$ m from its center? N $($b$)$ What centripetal force $($in N$)$ does she need to stay on an amusement park merry$-$go$-$round that rotates at $3\mathrm{.}00$ rev $/$ min if she is $9\mathrm{.}00$ m from its center? N $($c$)$ Compare each force with her weight. $[$ force from $($a$)/$ weight $=$; force from $($b$)/$ weight $=]$ At its peak, a tornado is $68\mathrm{.}0$ m in diameter and carries $390$ km $/$ h winds. What is its angular velocity in revolutions per second? rev $/$ s