| R m v |
 |
| Itotal |
| m v |
|
| cMR + mR |
Sarah, with mass m and velocity v, runs toward a playground 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 a constant 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 linear momentum p can be transformed to an angular momentum L much like a force is turned into a torque.
L = r × p
The magnitude of the angular momentum is L = 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:
Total angular momentum before = total angular momentum after
Rmv + 0 = Itotal ωf
Itotal = The moment of inertia of the merry-go-round plus Sarah's moment of inertia.
Itotal = cMR2 + mR2
| Therefore: | ωf | = |
|
= |
|
Numerical example
Let's say m = 25 kg; v=4 m/s; M = 50 kg; R = 2 m; c = ½
| ωf | = |
|
= | 1 rad/s |