A merry$-$go$-$round is being ridden by $2$ children; one is $16\mathrm{.}5$ kg$,$ and the other one is $21\mathrm{.}5$ kg $($see

below$).$ Both are sitting at the outside edge of a ring that has a mass of $57\mathrm{.}5$ kg and radius of $1\mathrm{.}3$

meters. Their father gets them started by pushing at the outside edge with a tangential force of $288$

Newtons through an angular distance of $100.$

a$)$ In an ideal situation without friction from the bearing in the middle. Determine the angular

speed of the ride be after the push from their father.

b$)$ If the final angular speed is $2\mathrm{.}82$ rad$/$sec$,$ determine the frictional torque in the ride.

c$)$ Given the frictional torque in b$),$ how many revolutions will the ride make before it comes to a

stop after the father's force is removed?