Understanding Angular Momentum in Rigid Body Rotation

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Discussion Overview

The discussion revolves around the concept of angular momentum in the context of rigid body rotation, specifically addressing why angular momentum can be expressed as the product of moment of inertia and angular velocity only for bodies rotating about an axis of symmetry. The scope includes theoretical explanations and clarifications suitable for high school physics students.

Discussion Character

  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions why angular momentum can only be expressed as the product of moment of inertia and angular velocity for rigid bodies rotating about an axis of symmetry.
  • Another participant points out that moment of inertia is a tensor and that when a body rotates about a non-symmetry axis, the angular momentum does not align with the axis of rotation.
  • A participant expresses confusion regarding the explanation and requests a more thorough clarification suitable for a high school audience.
  • Another participant seeks an example to illustrate the concept of angular momentum not aligning with the axis of rotation when the axis is not a symmetry axis.

Areas of Agreement / Disagreement

Participants exhibit uncertainty and seek clarification on the topic, indicating that multiple competing views remain regarding the explanation of angular momentum in non-symmetrical rotations.

Contextual Notes

There is a lack of consensus on the explanation of angular momentum in non-symmetrical rotations, and participants have noted that textbooks may not provide sufficient detail on the topic.

mr.physics
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Why can only the angular momentum of a rigid body rotating about an axis of symmetry be expressed as the product of the body's moment of inertia and its angular velocity?
 
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The "moment of inertia" is actually a tensor. If a body is rotated about an axis that is not a symmetry axis (or, more generally, an axis for which the tensor is not diagonal), the angular momentum in not in the direction of the axis of rotation.
This is discussed in Mechanics terxtbooks.
 
Hmm.
I still don't really understand why not and my textbook doesn't supply much of an explanation.
Could someone please explain more thoroughly in terms a high school physics student might be privy to?
 
clem said:
If a body is rotated about an axis that is not a symmetry axis [..] the angular momentum [is] not in the direction of the axis of rotation.
Would you describe (or cite) an example of that?
 

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