3
$\begingroup$

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?

$\endgroup$
3
  • $\begingroup$ 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

4
$\begingroup$

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.

$\endgroup$
2
  • $\begingroup$ 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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.