Deriving Møller's Relativistic Minimum Radius for Rotating Bodies

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Discussion Overview

The discussion revolves around the derivation of Møller's formula for the relativistic minimum radius of a rotating body. Participants are seeking resources or derivations related to this concept, which is situated within the context of relativistic physics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Homework-related

Main Points Raised

  • One participant requests a derivation or reference for Møller's formula, expressing frustration over the lack of accessible information.
  • Another participant suggests specific references, including Møller's original works and a textbook, indicating that these sources might contain the needed derivation.
  • Some participants express dissatisfaction with existing sources, noting that they only present conclusions without derivations.
  • There is a suggestion to consult a specific advanced book on relativity, although one participant expresses reluctance to purchase it for a single question.
  • A participant shares a Wikipedia link, but others argue that it does not provide the derivation they are seeking.
  • Concerns are raised about the implications of a minimum radius for spinning objects in a fully relativistic context, with one participant questioning the reasoning behind such a concept.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the availability of a derivation for Møller's formula. Multiple competing views exist regarding the adequacy of the sources provided, and the discussion remains unresolved.

Contextual Notes

Limitations include the potential inaccessibility of certain texts and the reliance on references that may not provide the desired derivation. There is also uncertainty regarding the theoretical implications of a minimum radius in relativistic physics.

michael879
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Can someone either derive or point me to a derivation of Møller's formula for the relativistic minimum radius of a rotating body? I've been searching for about an hour and it's driving me crazy!

The only "minimum radius" equation I've seen imposes the speed limit c on a classical rotating body (v = L/mR < c). This is only semi-relativistic since it takes L=r x p and p=mv. The two results are identical, but from the references I can find Møller's formula is supposedly fully relativistic...
 
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anyone? I wouldve expected this to be a quick answer.. To bad I posted this seconds before they shut the site down for migration >.<
 
Try:
C. Moller, Commun. Dublin Inst. Adv. Stud., A5, 1 (1949).
C. Moller, ”The Theory of Relativity”, 2nd ed. (Oxford University Press, 1972), p. 176.

The second (textbook) reference will probably be easier to find. The secondary source for these references was http://www.phys.lsu.edu/faculty/oconnell/PDFfiles/311. Rotation and Spin in Physics.pdf in the section quoted below.
This is also connected to the fact that, as Moller has shown [12, 13], a spinning body has a minimum radius equal to ...
 
Thanks pervect, I did come across Moller's stuff but I don't have access through my school (they're too old). I'll check out that second source tho
 
>.< yea your source is just like all the ones I found! They reference Moller's work but only show the conclusion...
 
michael879 said:
Thanks, but I'd really rather not buy an entire textbook for the answer to this one question!
Sorry, let me clarify that a little:

I already have plenty of textbooks on relativity, so buying a new one just for this question seems ridiculous. If there really is no accessible derivation can somebody who has the textbook just sketch the argument out for me?
 

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