Alternative Equation of Motion

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Discussion Overview

The discussion centers around an alternative equation of motion in classical mechanics, specifically examining the implications of this equation on the validity of Newton's laws in different reference frames, particularly non-rotating frames. Participants explore the conditions under which Newton's laws apply and the nature of inertial versus non-inertial reference frames.

Discussion Character

  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant presents an equation of motion that suggests a particle can have non-zero acceleration without a net force acting on it, challenging the traditional understanding of Newton's laws.
  • Another participant agrees that Newton's laws hold true in inertial reference frames, indicating that this is a standard definition of such frames.
  • A different participant asserts that the proposed equation can be applied in any non-rotating reference frame without introducing fictitious forces, suggesting a broader applicability.
  • One participant questions the underlying assumption of a universal inertial frame, arguing that if frame S is fixed to particle S, then there should be no forces acting on S, implying a flaw in the reasoning presented.
  • Another participant expresses uncertainty about the intent behind the original post, suggesting that if it is a proposal for a new method of calculating acceleration, it may not be particularly novel.

Areas of Agreement / Disagreement

Participants exhibit disagreement regarding the implications of the proposed equation on Newton's laws and the nature of inertial frames. While some affirm the validity of Newton's laws in inertial frames, others challenge the assumptions made in the discussion.

Contextual Notes

The discussion involves assumptions about the nature of reference frames and the conditions under which Newton's laws apply. There are unresolved questions regarding the definitions of inertial and non-inertial frames and the implications of the proposed equation on these concepts.

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In classical mechanics, the acceleration \vec{a}_A of a particle A relative to a reference frame S (non-rotating) fixed to a particle S, is given by the following equation:

\vec{a}_A = \frac{\vec{F}_A}{m_A} - \frac{\vec{F}_S}{m_S}
where \vec{F}_A is the net force acting on particle A, m_A is the mass of particle A, \vec{F}_S is the net force acting on particle S, and m_S is the mass of particle S.

In contradiction with Newton's first and second laws, from the above equation it follows that particle A can have non-zero acceleration even if there is no force acting on particle A, and also that particle A can have zero acceleration (state of rest or of uniform linear motion) even if there is an unbalanced force acting on particle A.

On the other hand, from the above equation it also follows that Newton's first and second laws are valid in the reference frame S only if the net force acting on particle S equals zero. Therefore, the reference frame S is an inertial reference frame only if the net force acting on particle S equals zero.
 
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Yes, Newton's laws hold true in inertial reference frames. This is one way to define an inertial reference frame..
 
Matterwave said:
Yes, Newton's laws hold true in inertial reference frames. This is one way to define an inertial reference frame..


This equation of motion can be applied in any non-rotating reference frame (inertial or non-inertial) without the need to introduce fictitious forces.

The forces acting on a reference frame determines if the reference frame is inertial or non-inertial.
 
Looks to me that hidden behind all that junk is the assumption that there is some universal inertial frame of reference. If you work in frame S and this frame is "fixed to a particle S" than in frame S there are no forces acting on S. Everything else after that is nonsense.
 
I'm not sure if you're posting this because you're confused or because you want to propose this as a new way of calculating acceleration. If it's the former you seem to have answered your own question (Newton's laws are valid in inertial frames which are frames with no net acceleration) but if it's the latter I don't think this is particularly new.
 

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