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