Angular Momentum: Li = Lf Equation for 2 Cylinders

[asz304]

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

 

[dreit]

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.