Five$-$year$-$old Kyra is riding on a carousel. The carousel $($with all of its passengers$)$ can be modeled as a uniform cylinder of mass $8900$ kg and diameter $12$ m $.$ While it is spinning at its top angular speed, Kyra's mom measures that it takes $6\mathrm{.}7$ seconds for Kyra to go all the way around once. Unfortunately, the carousel's motor breaks and it begins to slow down with constant acceleration. After $2\mathrm{.}5$ revolutions, the carousel comes to rest. Assume that the only torque acting on the carousel while it's slowing down is due to friction.

$[1]$ What is the angular velocity of the carousel while it is running, before the motor breaks?

$[2]$ What is the magnitude of the torque due to friction acting on the carousel while it is slowing down?

$[3]$ Kyra is bitterly disappointed that the ride broke. Her mother, a mechanical engineer, starts to wonder whether the adults present could have kept the ride going if they had promptly jumped up and pulled on the carousel. If there were eight adults and they applied equal forces tangentially at the outside edge of the carousel, how much force would each adult have needed to apply to overcome the frictional torque and keep the carousel rotating at constant angular velocity?

$[4]$ How fast would they have needed to be walking$/$running around the carousel as they applied this force?