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 ω_f. If Sarah's initial velocity is tangent to the circular merry-go-round, 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 = cMR² + mR²

Therefore:

ωf

=

R m v Itotal

=

m v cMR + mR

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

ωf

=

100 50 + 50

=

1 rad/s