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Newton did not discover F =ma and second law of motion


sharma, ajay


Research Papers


Mechanics / Electrodynamics



Date Published:

February 26, 2014




Newton, Euler , F=ma


AbstractNewton has given second law of motion as “alteration in motion is proportional to impressed force” in the Principia at page 19; mathematically it is F =k(v-u), where k is coefficient of proportionality with dimensions MT-1. The same equation follows from Definition IV of force in the Principia. But this equation is completely neglected. In the existing literature statement “ rate of change of momentum is proportional to impressed force” is used; mathematically, F =ma is regarded as pervasive equation for Newton’s second law . It was never given by Newton, but credited to Newton unscientifically. In 1750 Swiss mathematician Euler gave force as F=ma/n (where n constant and depends upon unity of measure). Further, Euler using extrinsic references frames (a system of three orthogonal Cartesian axes), gave mathematical equation F =2md2s/dt2 =2ma (the coefficient 2 depended on the unity of measure). Euler capriciously divided RHS by 2 to obtain F =ma, which contravenes the definition of equation. Thus in order to obtain all-encompassing mathematical form of Newton’s second law (F=ma) arbitrariness is the basis. The dimensional analysis was initiated by Fourier in 1822, unit of force dyne was defined in 1861 and newton in 1948. So science has progressed slowly, now it is time for unanimously answer the unaddressed questions. For example which is the logical equation of force F =k(v-u), F=ma/n, F =2ma or F=ma.

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