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Second Law of Motion, F=ma, was discovered after 48 years of death of Newton


sharma, ajay


Research Papers


Mechanics / Electrodynamics



Date Published:

July 4, 2014




Newton, Euler, F=ma


Neither prevalent definition nor equation F=ma was given by Newton , but credited to Newton unscientifically. Euler gave three equations of force F=ma/2 or F=ma/n in 1736, F=2ma in 1750, (the coefficient 2 depended on the unity of measure) and F=ma in 1775 in different ways. Which of three should be regarded as equation of force? Realistically F =ma is speculated not derived by Euler. Further, F=ma is used to derive rest mass energy equation (E0=M0c2 ), but if F =2ma , F=ma/2 are used then equations for rest mass energy become E0=2M0c2 and E0=M0c2/2. These aspects are undiscussed yet. If the magnitudes equations of force F=ma and F=2ma are equal in magnitude then 1=2, which is not true. Or for equality of force, it has to be assumed that Euler capriciously divided or multiplied right hand sides by 2 to obtain F =ma. There is no other way to obtain F=ma from F=2ma and F=ma/2. The coefficients must be same in both equations of force i.e. 2. Euler used two primary or fundamental units L (length) and F( force), hence value of coefficient is 2. The systems of primary units L (length)-F(force) –T(Time ) and L (length)- M(mass) –T(Time ) were introduced in the following century. Thus F=ma may be understood as a postulate, and must be credited to Euler who speculated it. The Principia‘s second law of motion i.e. F =k(v-u) is not discussed at all.

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