Difference between Moment-of-Momentum and Angular Momentum

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Discussion Overview

The discussion revolves around the concepts of moment-of-momentum and angular momentum, particularly in the context of an extended body and its decomposition into components. Participants explore the definitions and interpretations of these terms as they relate to the angular momentum of a system of particles.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant describes the angular momentum of an extended body as a sum of the moment-of-momentum of an equivalent particle and the angular momentum around the center of mass.
  • Another participant questions the definition of "moment-of-momentum" and seeks clarification on the terms used in the equation presented.
  • A participant confirms the interpretation of the terms on the right-hand side of the equation, asserting that the first term relates to the angular momentum of the equivalent particle with respect to the origin, while the second term pertains to the angular momentum of individual particles around the center of mass.
  • One participant notes that "moment-of-momentum" is often loosely referred to as angular momentum, which can lead to confusion, and states that they are identical only in special cases.
  • Another participant suggests looking up "angular momentum of a system of particles" for further understanding and agrees that the term "moment of momentum" is unusual but makes sense in context.
  • There is a discussion about the language of the book being referenced, confirming it is in English.

Areas of Agreement / Disagreement

Participants generally agree on the meanings of the terms discussed, but there remains some uncertainty regarding the terminology and its implications. The discussion does not reach a consensus on the clarity of the term "moment-of-momentum."

Contextual Notes

There are unresolved questions about the definitions and usage of "moment-of-momentum" versus angular momentum, as well as the implications of their differences in various contexts.

tomwilliam2
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I've been reading a book that talks about the angular momentum of an extended body around a point 0 (H_0) being made up of the moment-of-momentum of an equivalent particle (representing the total mass at the centre of mass) with respect to the point 0 and the angular momentum around the centre of mass, C:
##\mathbf{H}_0 = M\mathbf{h}_0 + \mathbf{H}_C##
I've never seen this second term on the RHS before. Is it basically saying that there is the angular momentum of the e.p. with respect to the origin, but then there's also the angular momentum of the individual particles in the extended body around the centre of mass?
 
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So what is your question? This decomposition of the total angular momentum is quite standard.
But what is "moment-of-momentum"?
 
nasu said:
So what is your question? This decomposition of the total angular momentum is quite standard.
But what is "moment-of-momentum"?
Thanks. My question was what each of the terms of the RHS corresponded to. It was my understanding that the first term related to the angular momentum of the equivalent particle with respect to the origin, while the second term was the angular momentum of the individual particles around the centre of mass of the extended object. Is that a correct interpretation?
Moment-of-momentum is defined (by the author of the book I'm reading) as
##m\mathbf{h}_0 = \mathbf{r} \times m\mathbf{v}##
"moment-of-momentum is often loosely referred to as 'angular momentum' ##\mathbf{H}_0##. This can lead to some confusion. Only in special cases are the two identical, such as when there is only one particle."
 
Yes, these are the meanings of the terms.
If you want to see where they come from, look up "angular momentum of a system of particles".
For example here, see under "colelction of particles":
https://en.wikipedia.org/wiki/Angular_momentum#Collection_of_particles

Yes, you are right. The "moment of momentum makes sense. It is the moment of the linear momentum. It is just unusual.
Is the book you quote in English or you translate from a different language?
 
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nasu said:
Yes, these are the meanings of the terms.
If you want to see where they come from, look up "angular momentum of a system of particles".
For example here, see under "colelction of particles":
https://en.wikipedia.org/wiki/Angular_momentum#Collection_of_particles

Yes, you are right. The "moment of momentum makes sense. It is the moment of the linear momentum. It is just unusual.
Is the book you quote in English or you translate from a different language?
Thanks again.
The book is in English ("Spacecraft Systems Engineering" by Fortescue, Swinerd and Stark).
 

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