Sarah, with mass m and velocity v, runs toward a merrygoround and jumps on at its edge. Sarah and the merrygoround (mass M, radius R, and I = cMR^{2}) then spin together with angular velocity ω_{f}. If Sarah's initial velocity is tangent to the circular merrygoround, what is ω_{f}?
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 L_{i} = Rmv.
Applying angular momentum conservation: Rmv + 0 = I_{total} ω_{f}
Here I_{total} = cMR^{2} + mR^{2}
Therefore:  ω_{f}  = 

= 

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

=  1 rad/s 