Rotation about two axes and angular momentum

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Discussion Overview

The discussion revolves around the behavior of angular momentum in a system undergoing rotation about two axes. Participants explore the changes in angular momentum, particularly along the z-axis, and the implications of these changes on the system's dynamics. The focus includes theoretical considerations and interpretations of angular momentum conservation.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant questions how the magnitude of ##L_x## remains constant during the rotation about the y-axis, suggesting that the actual motion may differ from a simplified model.
  • Another participant proposes that ##L_z## could be zero, at least periodically, indicating uncertainty about its behavior over time.
  • A later reply confirms the initial state of angular momentum as ##\mathbf{L}=(L_x,L_y,0)## and assumes its conservation at later times, but does not clarify the conditions under which this holds.

Areas of Agreement / Disagreement

Participants express differing views on the behavior of angular momentum, particularly regarding the constancy of ##L_x## and the periodicity of ##L_z##. The discussion remains unresolved with multiple competing perspectives.

Contextual Notes

Participants do not fully address the assumptions underlying their claims, such as the conditions for conservation of angular momentum or the specifics of the rotational motion involved.

Kashmir
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IMG_20210709_103319.JPG

I've a body having initial angular velocity at ## t=0 ## as shown. The axis shown are fixed in inertial space and initially match with the principal axis. I want to find the infinitesimal change at ##t+\Delta t## in the angular momentum along the ##z## axis.

I've seen the following approach which I don't understand:
One contribution to change in ##L_z## is due to rotation about y axis. This causes ##L_x## to rotate and hence a component ##-L_x \Delta{_y}## appears.
IMG_20210709_105348.JPG

How do we know that ##Lx## will remain constant in magnitude? Also the actual motion won't be as is shown, in which the body simply goes around the y-axis while maintaining it's spin ##L_x##

A similar method is used here by Kleppner and Kolenkow here
IMG_20210709_112436.JPG
 
Last edited:
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May we expect Lz=0? At least periodic it seems.
 
anuttarasammyak said:
May we expect Lz=0? At least periodic it seems.
Initially?
 
Yes, and I assume ##\mathbf{L}=(L_x,L_y,0)## is conserved in later time.
 

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