Sam, whose mass is $36$ kg$,$ stands at the center of a $200$ kg merry$-$go$-$round that is rotating once every $2\mathrm{.}5$ s$.$ While it

is rotating, Sam walks out to the edge of the merry$-$go$-$round, $2\mathrm{.}0$ m from its center. What is the rotational period of the

merry$-$go$-$round when Sam gets to the edge?