A child pushes a merry$-$go$-$round that has a diameter of $4\mathrm{.}00$ m and goes from rest to an angular speed of $18\mathrm{.}0$ rpm in a time of $43\mathrm{.}0$s$.($a$)$ Calculate the average angular acceleration $($in rad$/$s$^2)$ of the merry$-$go$-$round. $($b$)$ Calculate the angular displacement $($in rad$)$ of the merry$-$go$-$round during this time interval. $($c$)$ What is the maximum tangential speed of the child if she rides on the edge of the platform?