I How Does the Book's Formula for Angular Momentum Differ from Mine?

AI Thread Summary
The discussion centers on the differences in calculating angular momentum for a disc between a user's method and a book's formula. The user calculates angular momentum using the equation L = I_x ω_x + I_y ω_y + I_z ω_z, while the book includes an additional term, L_s sin θ_y, suggesting a different approach. Questions arise regarding the initial conditions of the disc's rotation and the definitions of the angular velocity components and moments of inertia. Clarifications are sought on the user's calculations and the context of the disc's motion. Understanding these distinctions is crucial for accurate angular momentum analysis.
Kashmir
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A disc initially has angular velocities as shown
IMG_20210707_220620.JPG

It's angular momentum along the y-axis initially is ##L_s##
I tried to find its angular momentum and ended up with this:##L=I_{x} \omega_{x}+I_{y} w_{y}+I_{z} z_{z}##The z component of angular momentum is thus ##L_{z}=I_{z} \omega_{z}##

However I found a similar situation in a book
IMG_20210707_223058.JPG
IMG_20210707_221438.JPG


that writes the components of angular momentum along x as ##L_{x}=I_{x x} \frac{d \theta_{x}}{d t}+L_{s} \sin \theta_{y}##

The book has an additional term ##L_{s} \sin \theta_{y}## for the angular momentum which I don't.

Why am I wrong ?
 
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Your question is not completely clear. Perhaps the disc is initially spinning with an ## L_s ## and then given an additional rotation. Otherwise a magnetization of the disc could also make for an ## L_s ##, but in general ## L_s ## from any magnetization would be very small.
 
Are you asking for an expression for the angular momentum of a disk where the rotation axis is not perpendicular to the disk? Your drawing is not clear.

Are ##\omega_x, \omega_y## and ##\omega_z## the cartesian coordinates of ##\vec\omega##? How are ##I_x##, ##I_y## and ##I_z## defined? Can you describe your calculations?
 
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