Newton's third law in non-inertial frames

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Discussion Overview

The discussion centers on the validity of Newton's third law in non-inertial frames of reference, particularly in the context of rotating frames. Participants explore whether the law holds true when pseudo forces are introduced and how this relates to the second law of motion.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • Some participants question whether Newton's third law is valid in non-inertial frames, particularly in rotating frames, and whether the non-inertial nature of the frame violates the law.
  • One participant suggests that if the second law is assumed valid in non-inertial frames, pseudo forces may lead to violations of the third law.
  • Another participant asserts that the forces between two objects in contact remain equal and opposite regardless of the reference frame, implying that the third law holds true.
  • It is noted that the second law's applicability is contingent on the reference frame, and fictitious forces must be included in non-inertial frames to maintain consistency.
  • Some participants propose that Newton's third law can be used to determine whether a frame is inertial by checking the consistency of interaction forces with the second law.

Areas of Agreement / Disagreement

Participants express differing views on the applicability of Newton's third law in non-inertial frames, with some asserting its validity while others highlight potential violations due to pseudo forces. The discussion remains unresolved regarding the conditions under which the law holds.

Contextual Notes

Participants reference the dependence of the second law on the reference frame and the introduction of fictitious forces in non-inertial frames, but do not reach a consensus on the implications for the third law.

Debdutta
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Is Newton's third law valid in non-inertial frames? For example, in a rotating frame of reference, can Newton's third law still be applied? Or does the non-inertial character of the frame violate it?
 
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Debdutta said:
Is Newton's third law valid in non-inertial frames?

Only if the second law is not valid. But usually the second law is assumed to be valid in non-inertial frames. This results in pseudo forces violating the third law.
 
Welcome to PF!

Hi Debdutta! Welcome to PF! :smile:
Debdutta said:
Is Newton's third law valid in non-inertial frames?

As between two objects in contact?

Yes, the forces will still be equal and opposite.
 
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The forces acting between two objects do not depend on the coordinate system or referemce frame you use to measure them. So the third law always holds.

The second law is different: the apparent accelerations that you measure DO depend on the reference frame, hence the second law does not hold in a accelerating frame unless you add another term to the equation (a.k.a a fictitious force) to compensate for the acceleration of the frame.
 
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So my next question is, can we assume that Newton's Third Law is still valid for interacting objects in any frame to test whether it is actually an inertial frame or not, that is, the first two laws of Newton hold or not?
 
Debdutta said:
So my next question is, can we assume that Newton's Third Law is still valid for interacting objects in any frame to test whether it is actually an inertial frame or not, that is, the first two laws of Newton hold or not?
Yes. You can always assume that the interaction forces between objects obey Newton's Third Law. If the sum of all interaction forces on an object and its coordinate acceleration are not consistent with Newtons Second Law, then you know that your frame is not inertial.
 
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