Jumping on a Merry-Go-Round

Sarah, with mass m and velocity v, runs toward a merry-go-round and jumps on at its edge. Sarah and the merry-go-round (mass M, radius R, and I = cMR2) then spin together with angular velocity ωf. If Sarah's initial velocity is tangent to the circular merry-go-round, what is ωf?

Apply angular momentum conservation. Sarah's angular momentum before the collision equals the angular momentum of the system after the collision.

Sarah's initial angular momentum is L = r × p = r p sin θ, where θ is the angle between r and p.

In this example Sarah's initial angular momentum is Li = Rmv.

Applying angular momentum conservation:   Rmv + 0 = Itotal ωf

Here  Itotal = cMR2 + mR2
Therefore: ωf =
R m v
m v
cMR + mR

Numerical example: m = 25 kg; v=4 m/s; M = 50 kg; R = 2 m; c = ½

ωf =
50 + 50
= 1 rad/s