# Is Newton's third law independent of the frame being inertial or non-inertial?

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?

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

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.
• 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. Dec 13, 2021 at 16:54