When you have already shown the transformation formulas for speed and acceleration of a point mass in two reference systems (Oxyz) and (O’x’y’z’) that move with a constant speed relative to each other. (v=v’+V’ and a=a’ with V the speed at which O’ moves in the (Oxyz) reference frame and all this of course vectorially.)
Now you can show that Newton’s second law remains unchanged:
Suppose a particle with mass m is subjected to a force:
F=ma =m.a’=F’ (also all this vectorial)
But now the question is how exactly you can deduce the consistency of the third law from this.
Kind regards,
Tim
Answer
Suppose it wasn’t. For example, at the level of an atom, the nucleus attracts an electron with a certain force, but the electron attracts the nucleus with the same force. The sum of all those internal forces over the whole atom is therefore zero and the atom cannot accelerate under the influence of those internal forces. If those forces in another coordinate system were not equal, the atom can accelerate without an external force, which is in contrast to the first and second laws.
Answered by
Prof Walter Lauriks
Physics Acoustics
Old Market 13 3000 Leuven
https://www.kuleuven.be/
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