Problem $7.$ A merry$-$go$-$round is initially rotating clockwise at

$\backslash$omega $\_(0)=60$ revolutions per minute $($rpm$).$ Two daring children, each

with a mass m$=10$kg$,$ attempt to jump onto the merry$-$go$-$

round. Both run tangentially toward opposite ends of the merry$-$

go$-$round at equal speeds of $1($m$)/($s$).$ The child at point A

successfully lands on the merry$-$go$-$round. The child at point B

misses and is knocked off by a bar going back in the opposite

direction at a speed of $0\mathrm{.}2($m$)/($s$).$ The merry$-$go$-$round has a radius

R$=2$m and a mass M$=50$kg$.$ It can be modeled as a uniform

disk.

What is the final angular velocity of the merry$-$go$-$round?