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Contributions of Newton and Euler towards F=ma


sharma, ajay


Research Papers


Mechanics / Electrodynamics



Date Published:

February 7, 2014






Newton’s second law of motion …….‘The alteration of motion is ever proportional to the motive force impress'd; and is made in the direction of the right line in which that force is impress'd.’ remained unchanged in all three editions ( 1687,1713 and 1726) of the Principia. Newton did not give any equation based upon second law either in algebraic or differential forms. In 1750 Swiss mathematician Leonhard Euler independently i.e. using extrinsic references frames (a system of three orthogonal Cartesian axes), gave mathematical equation F =md2s/dt2 =ma. Euler’s equation is incorrectly regarded as equation for the Principia’s second law of motion. Now an attempt has been made to derive equation of motion for the Principia’s second law of motion, using various relevant terms ( absolute motion, relative motion, celerity as motion , definition of force etc. ) defined by Newton is the Principia. Obviously mathematical equation on the Principia’s second law of motion, turns out to be F =k(v-u), k has dimensions MT-1. The dimensional analysis was initiated by Fourier in 1822 , unit of force dyne was defined in 1861 and newton in 1948. Thus there are two laws of motion i.e. the Principia’s second law of motion F = k(v-u) , and Euler’s law of motion F =ma. Thus Newton’s second law which is taught in standard literature, in fact is statement for Euler’s equation F=ma. Newton’s statement as given in the Principia page 19 is neglected completely.

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