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Physics/Mathematical Proof of Newton's Third law

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Question
Sir can you explain me the Proof of newtons's third law Mathematically???
This law is so intuitive that i am unable to deduce it mathematically..

Answer
Well, since the forces considered by Newton are gravitational or electrostatic in nature, you can derive it from Coulomb's Law or Newton's law of gravitation.  Both feature constants, object quantities (mass or charge), and a 1/r^2 form.  Since multiplication of the material properties (m or q) is a commutative process, this leads us to Newton's third law.  You can write out the full force equations if you want and show that the force of one mass on another via gravitation (for an example) is equal to the force of the second mass on the first, but it seems trivial.  The fully relativistic versions of Newton's law would be tricky, even for a specialist in that area, and I've never seen anyone bother.

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Dr. Stephen O. Nelson

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I can answer most basic physics questions, physics questions about science fiction and everyday observations of physics, etc. I'm also usually good for science fair advice (I'm the regional science fair director). I do not answer homework problems. I will occasionally point out where a homework solution went wrong, though. I'm usually good at explaining odd observations that seem counterintuitive, energy science, nuclear physics, nuclear astrophysics, and alternative theories of physics are my specialties.

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I was a physics professor at the University of Texas of the Permian Basin, research in nuclear technology and nuclear astrophysics. My travelling science show saw over 20,000 students of all ages. I taught physics, nuclear chemistry, radiation safety, vacuum technology, and answer tons of questions as I tour schools encouraging students to consider careers in science. I moved on to a non-academic job with more research just recently.

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Ph. D. from Duke University in physics, research in nuclear astrophysics reactions, gamma-ray astronomy technology, and advanced nuclear reactors.

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