Friday, 28 September 2018

newtonian mechanics - Can one of Newton's Laws of motion be derived from other Newton's Laws of motion?


Can one derive Newton's


second and third laws from the first law or


first and third laws from the second law or


first and second laws from the third law


I think Newton's laws of motions are independent to each other. They can not be derived from one another. Please share the idea.



Answer




The modern interpretation of Newton's First Law is about the existence of inertial reference frames, mainly to solidify the idea that such coordinate systems exist and are important.


However, I sincerely doubt this is what Newton himself had in mind when he postulated his laws. Historically, Newton probably introduced his first law to put emphasis on the fact that moving bodies do not slow down by their own accord (as was common wisdom at the time). So yes, the first law in this context can certainly be derived from the second law by setting F=0. In fact I doubt Newton even had an idea of what an inertial frame was (though it probably could have been explained to him with relative ease).


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