Is the Moment of Inertia strictly different

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Discussion Overview

The discussion revolves around the moment of inertia of two bodies with mass distributed along a line, specifically whether their moments of inertia about their respective centers of mass are strictly different or if they can be the same. The scope includes theoretical considerations and mathematical reasoning related to the definition and calculation of moment of inertia.

Discussion Character

  • Exploratory
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant seeks proof regarding whether the moment of inertia for two bodies with mass distributed along a line is strictly different.
  • Another participant questions the clarity of the original question, particularly regarding the meaning of mass distribution along a line.
  • A participant clarifies that the bodies are one-dimensional, similar to ropes, and consist of discrete masses rather than a continuous distribution.
  • There is a discussion about deriving the total moment of inertia by integrating the moments of inertia of the individual masses.
  • One participant asks if two different mass distributions can yield the same moment of inertia.
  • Another participant asserts that it is indeed possible for two different mass distributions to have the same moment of inertia.
  • There is a reiteration of the question regarding whether the moment of inertia values are strictly different for two different bodies.
  • A participant prompts another to consider the definition of moment of inertia in their inquiry.

Areas of Agreement / Disagreement

Participants express differing views on whether the moment of inertia for two bodies can be the same, indicating a lack of consensus on the matter.

Contextual Notes

The discussion includes assumptions about the nature of mass distribution and the implications of the definition of moment of inertia, which remain unresolved.

deep838
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I would like to know if there is any proof as to whether the moment of inertia for two bodies (the masses of each body are distributed on a line) about their respective center of masses, is strictly different. If not, can anyone provide me a link to where the work is computed.
 
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Your question is somewhat vague.

How is the mass of each body 'distributed on a line'? What does that mean?
 
I mean to say that the bodies are not 2 dimensional, they only have length.. Like a rope. Only the distribution is not continuous, it is made of a number of masses
 
deep838 said:
I mean to say that the bodies are not 2 dimensional, they only have length.. Like a rope. Only the distribution is not continuous, it is made of a number of masses
You derive the total moment of inertia by integrating (adding up) the moments of inertia, of these masses.
 
A.T. said:
You derive the total moment of inertia by integrating (adding up) the moments of inertia, of these masses.
Yes, but is that value strictly different for two different bodies? Or can two mass distribution have the same moment of inertia?
 
deep838 said:
Or can two mass distribution have the same moment of inertia?
Of course they can.
 
deep838 said:
Yes, but is that value strictly different for two different bodies? Or can two mass distribution have the same moment of inertia?

Have you actually looked at the definition of MI?
 

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