Center of rotation of a free rod

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Discussion Overview

The discussion revolves around the dynamics of a free rod on a frictionless surface when subjected to an external force at various points. Participants explore the implications of hitting the rod at different locations, particularly concerning the center of mass (CM) and the center of rotation, as well as the validity of conservation laws in these scenarios.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant suggests that hitting the rod at its tip causes it to translate and rotate around its CM, while questioning the behavior when struck at other points.
  • Another participant proposes that the center of rotation is a relative concept, similar to the arbitrary nature of axes, indicating that different points yield different moments of inertia.
  • A participant seeks clarification on the path of the center of mass if the rod rotates around a point other than its CM, raising questions about momentum conservation in such a scenario.
  • One reply discusses the implications of the center of mass rotating around a "center of rotation" that moves in a straight line, noting that this description may not represent an inertial reference frame.
  • Another participant expresses confusion regarding the concept of an "instant center of rotation" and its relation to forces not acting through the center of mass, asking for a clearer explanation without ambiguity.
  • A later reply challenges the clarity of the questions posed, suggesting that the phrasing may hinder productive discussion.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the behavior of the rod when struck at points other than the CM, with multiple competing views on the nature of rotation and the implications for conservation laws remaining unresolved.

Contextual Notes

Participants express uncertainty regarding the definitions and implications of the center of rotation and the instant center of rotation, as well as the conditions under which conservation laws apply. The discussion reflects a range of interpretations and assumptions that are not fully clarified.

alba
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Suppose we have a free rod on a frictionless surface: if we hit it on a tip it will translate and rotate around its CM.

What happens if we hit it at any other point between tip and CM? will it still rotate around CM?, if not, is it easy to find the center of rotation?

If not, are the 3 conservation laws still valid to find the angular velocity? I should say no because if the center is not at CM the rotation will be asymmetric.

Thanks a lot
 
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I'm not sure, but i think that the rotation center is a relative concept' just as the origien of the axe's is arbitrary.
for each point you will get a diffrent moment of innertia.
 
alba said:
Suppose we have a free rod on a frictionless surface: if we hit it on a tip it will translate and rotate around its CM.

What happens if we hit it at any other point between tip and CM? will it still rotate around CM?
Suppose that the rod rotated around some point other than its CM. In other words, assume that a hypothetical center of rotation were translating and the rod was rotating around it. Can you describe in ordinary non-mathematical terms the path that the center of mass would be following?

If the center of mass follows such a path, would momentum be conserved?
 
If i understand you correctly, the center of mass will rotate around the "center of rotation" which is a point that moves in a straight line. I think that the problem with this (legitimate) description of the system. Is that it is not an inertial reference frame.
 
jbriggs444 said:
Suppose that the rod rotated around some point other than its CM. In other words, assume that a hypothetical center of rotation were translating and the rod was rotating around it. Can you describe in ordinary non-mathematical terms the path that the center of mass would be following?If the center of mass follows such a path, would momentum be conserved?
I know the rod should always rotate around CM, but I asked becaause I fount this post on the web at SE : http://physics.stackexchange.com/qu...ct-and-start-purely-rotating-it/174171#174171 which seem to contrast with the other answer.

Can you explain what is an " instant center of rotation." ?and what does it mean that :".. a force not through the center of mass will rotate the body about a specified point."? what is the specified point, the instant center?

Please do not answer in riddles.
 
If you do not want an answer to the question you asked, ask a different question.
 

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