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Many playgrounds used to have roundabouts (also known as merry-go-rounds) for kids. They were fun to play on ​but easy to get hurt falling off of, so most are gone now.

A 50 kg roundabout with a radius of 1.5 m is spinning at 0.75 revolutions/second on a frictionless axis. A 45 kg child runs to jump onto the roundabout. The child is running at 3 m/s directly tangent to the outer edge of the roundabout, in the same direction as the roundabout is spinning, when he jumps onto the outer edge of the roundabout and holds on.

What is the rotational speed of the roundabout+child after the child has jumped on?

A

${\omega}_f=1.5\text{ }rad/s$

B

${\omega}_f=3.0\text{ }rad/s$

C

${\omega}_f=4.0\text{ }rad/s$

D

${\omega}_f=4.7\text{ }rad/s$

E

${\omega}_f=5.0\text{ }rad/s$

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