It is known that for Newton's second law to be valid it is fundamentally necessary that the system under study be an inertial reference, which automatically creates a direct dependence of the second law with Newton's first law. But does Newton's third law depend on the inertial frame or is it valid for any inertial or non-inertial system?

  • $\begingroup$ The third law is basically momentum conservation, so it won't hold in a non-inertial frame. $\endgroup$
    – J.G.
    Dec 13, 2021 at 14:44
  • $\begingroup$ @J.G. what have you to say about Ranjeet Tate's answer here: quora.com/…. $\endgroup$
    – Bob D
    Dec 13, 2021 at 16:08
  • $\begingroup$ @BobD The occasional typo aside, Tate's calculations rescue the third law by modifying the second. $\endgroup$
    – J.G.
    Dec 13, 2021 at 16:13

1 Answer 1


Third law does not hold in non-inertial frame. Let there be non-inertial frame moving with constant acceleration $\mathbf a$ with respect to inertial frame.

In that non-inertial frame, every body will experience apparent force $-m \mathbf a$ where $m$ is mass of the body. This apparent force has no counterpart.

  • $\begingroup$ What do you mean is that in a non-inertial frame where fictitious forces arise there will not be a reaction to these forces? Well, let's suppose two people on top of a car with acceleration a. If one person pushes the other, shouldn't there be an action and reaction between them even though they are on top of the accelerated car? $\endgroup$ Dec 13, 2021 at 16:41
  • 1
    $\begingroup$ Yes, the action-reaction force pairs that are present in inertial frame will be present also in non-inertial frame and for these, the third law still holds. But in non-inertial frame there will also appear "inertial" forces $-m\mathbf a$ which are without action-reaction counterparts, so third law does not hold for those. $\endgroup$ Dec 13, 2021 at 16:54

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