Why Newton’s Second Law is not F=ma

Resumo

The second law enunciated by Isaac Newton in the Principia is not equivalent to , as it is popularly known. The latter was described by Leonhard Euler, in 1752. However, for some historians, this formulation would be implicit in the statement proposed by Newton, and in this way,  is considered by some of them only as a mathematical reformulation of Newton's law. In this paper, we discuss reasons for the non-equivalence of these laws, as well as aspects that lead to this confusion of interpretations; we also discuss limitations of newtonian mechanics, which are about mathematical method, natural coordinates, and Newton's conceptions of force. Finally, we indicate the elements not covered by Newton's mechanics, thus showing that, in fact,  is a much more general law than that proposed by Newton.