Angular Momentum: Li = Lf Equation for 2 Cylinders

AI Thread Summary
The discussion centers on the conservation of angular momentum for two cylinders, where the first cylinder with moment of inertia I1 rotates at angular speed w1 and the second cylinder with moment of inertia I2 drops into it, resulting in a combined angular speed w2. The relevant equation is established as Li = Lf, leading to the formula I1 * w1 = (I1 + I2) * w2. Participants express uncertainty about the application of the moment of inertia formula I=(1/3)ML^2 and its modification for the second cylinder. The conversation emphasizes understanding the conservation principle and correctly applying the moment of inertia in the context of the problem. Overall, the focus is on deriving the correct relationship for the system's angular momentum.
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Homework Statement


A cylinder with moment inertia I1 rotates around a vertical frictionless axle with angular speed w1. A second cylinder with moment of inertia I2, drops into the first cylinder, then the the two objects have a similar angular speed of w2. What is the formula for the two cylinders with the conservation of momentum?

Homework Equations


Li = Lf

The Attempt at a Solution


Not sure if I'm right but this was my formula:
Li = Lf
I1 * w1 = ( I2 + I1 ) w2

Li = I1 * w1
Lf = ( I2 + I1 ) w2
 
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Im just learning this now, but the equation that I would think of using for this problem would be I=(1/3)ML^2. Then modify the equation to take into account the second cylinder, but anyone else feel free to correct me.
 

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