Euler is an innovator of F =ma, Newton’s second law gives F = KdV; F =ma may be obtained from Newton’s law by logically modifying it

• Published in: E3S web of conferences 2024, Vol.540, p.14005
• Main Author: Sharma, Ajay
• Format: Article
• Language: English
• ISSN: 2267-1242; 2267-1242
• DOI: 10.1051/e3sconf/202454014005

There are two distinct forms of Newton’s second law of motion (1686) i.e. original or Principia’s form of (change in motion is proportional to impressed force, F = KdV) and textbook form (rate of change of momentum is proportional to impressed force, F =ma). Newton neither gave acceleration nor F =ma, it is mentioned by IOP England, publications of the American Institute of Physics, etc. Truesdell has inconsistently pointed out in 1960 that Euler had given F =ma in 1752, but the truth is that Euler had given F=2ma in the said paper. Euler had also given various equations such as F =ma/n, F =2ma, F =ma/2g, F =ma etc.; but these are ignored by Truesdell. The exceptionally useful equation F =ma was given by Euler in 1775, and then succeeding scientists inconsistently tried to show that F =ma follows from the original form of the law. Consequently, some arbitrary assumptions are made, original form, F =KdV; and the fact that Euler gave F =ma are not mentioned in the standard textbooks. For comparison, Newton’s first law and third law (Reaction =-Action) are the same in the Principia and textbooks. In the existing literature, F =ma is obtained from Principia’s definition of NSLM, by replacing ‘change in motion’ equal to ‘rate of change of momentum’, but motion is not ascribed to any units and dimensions. If the original definition of Newton’s law is changed in a postulatory way i.e. ‘change in motion’ is replaced by ‘rate of change in momentum’ and ‘proportionality’ by ‘equality’; then F=ma is obtained from a modified equation without any arbitrary assumption. In 1893, Rouse Ball randomly altered Newton’s second law as a change in momentum [per unit time] is always proportional to the impressed force.