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Newton's Generalized Form of Second Law Gives F IOSR Journal Of Applied Physics (IOSR-JAP) e-ISSN: 2278-4861.Volume 13, Issue 2 Ser. I (Mar. – Apr. 2021), PP 61-138 www.Iosrjournals.Org Newton’s generalized form of second law gives F =ma Ajay Sharma Fundamental Physics Society. His Mercy Enclave, Post Box 107 GPO Shimla 171001 HP India Abstract Isaac Newton never wrote equation F =ma, it was clearly derived by Euler in 1775 ( E479 http://eulerarchive.maa.org/ ). Also, Newton ignored acceleration throughout his scientific career. It must be noted that acceleration was explained, defined and demonstrated by Galileo in 1638 (four years before birth of Newton) in his book Dialogue Concerning Two New Sciences at pages 133-134 and 146. Galileo defined uniform velocity in the same book at page 128 and applied it in Law of Inertia at page 195 in section The Motion of projectile. Descartes in book Principles of Philosophy (1644) and Huygens in his book Horologium (1673) used uniform velocity in defining their laws. Huygens also applied gravity in 1673 i.e. 13 years before Newton. Newton also defined first law of motion in the Principia (1686,1713,1726) in terms of unform velocity. Galileo, Descartes and Huygens did not use acceleration at all, as uniform velocity is used in law of inertia. Likewise, Newton ignored acceleration completely, even it was present in literature during his lifetime. So, it is distant point that Newton gave F=ma. The geometrical methods were the earliest method to interpret scientific phenomena. Now there are three main points for understanding of second law. Firstly, genuine equation based on second 2 2 law of motion F =kdV (it is obtained like F =Gm1m2/r or F m1m2, F 1/r or F dV) . But F = kdV is neglected by scientists completely . Secondly scientists related F =ma with second law. Then they tried to obtain, F =ma from second law, but it is not obtained from it. Thus, scientists made arbitrary assumptions that motion is momentum (mV), in fact motion is velocity. It does not serve the purpose. Then scientists assumed that change in motion (momentum) is equal to rate of change of momentum. As both sides of equation have different units, dimensions and magnitudes so these arbitrary assumptions are completely inconsistent. Thirdly to obtain F =ma from second law of motion is to change definition of the law so that acceleration appears in it. However, Newton has completely neglected acceleration. But now acceleration is arbitrarily brought in second law. The definitions of first and third laws of motion are quoted in the text books and standard references in the same way as given in the Principia. W W Rouse Ball has changed definition of second law of motion slightly i.e. used phrase change in momentum per unit time. Disagreeing with this I. Bernard Cohen given 4 equivalent equation forms of second law of motion. F =ma is inseparable part of physics, so it can be it can be obtained by changing the definition of the law, “The rate of change of momentum with time is equal to the motive force impressed; and is made in the direction of the right line in which that force is impressed.” Thus, we get F =ma from modified form of law, not from original form. --------------------------------------------------------------------------------------------------------------------------------------- Date of Submission: 18-03-2021 Date of Acceptance: 01-04-2021 --------------------------------------------------------------------------------------------------------------------------------------- I. Early Physics Gradually ancient minds tried to resolve various mysteries observed around him. There was no short cut, all processes took their own time. First feeling in human mind may be fear of some power which was beyond human’s physical and mental control …. thus, religion was developed in different ways in different regions. But eventually should converge at same point, so it must be cohesive force and not divisive. Earlier all branches of knowledge were fused together. The explosion of knowledge may be compared with ‘big bang’ which took place gradually and slowly. In ancient days man started expressing his insights on the sand or earth with diagrams, thus geometry was first mode of expressions. The science came into being, something we understand and also make others understand repeatedly. The converse is superstition, we cannot understand, cannot make others to understand. Initially all branches had one name, the natural philosophy. Natural philosophy was the philosophical study of nature and the physical universe that was dominant before the development of modern science. The various scientists extracted various branches such as mathematics, physics, chemistry, biology etc. emerged from natural philosophy. In physics Newton, Galileo and Aristotle were the pioneers, and numerous others who brought physics to current status. Earlier Aristotle (385-323BC) stated that force is required for movement of body. The table stops as soon force (may be push or pull) ceases to act on it. It is clearly observed even now due to presence of various resistive forces. The concept of inertia was alien to the physics of Aristotle. Aristotle, and DOI: 10.9790/4861-13020161138 www.iosrjournals.org 61 | Page Newton’s generalized form of second law gives F =ma his peripatetic followers held that a body was only maintained in motion by the action of a continuous external force. Aristotle implied that rest is natural tendency of body, it is disturbed when external force acts on body; and justified in above example. This doctrine was contested between admirers and critics for centuries. 1.1 Galileo’s Dialogue and Newton’s Principia are the pioneering books. Before Sir Isaac Newton’s masterpiece Mathematical Principles of Natural Philosophy [1,2] , Italian Galileo Galilei did pioneering work in process of initialization of physics. Italian has conducted some experiments with simple equipment about motion of bodies in first decade of 17th century (may be in1604), may be regarded as first genuine physicist. Galileo improved Aristotelian scientific views. Galileo defined uniform motion, acceleration and accelerated motion, he also applied uniform motion in formulating law of inertia (used in refined form as Newton’s First Law of Motion). Galileo [3] presented these experiments in his book Discorsie dimostrazioni matematiche intorno a due nuove scienze (Dialogues Concerning Two New Sciences) in 1638. It is translated by Henry Crew and Alfonso de Salvio. The book was written and published when Galileo Galilei was under house arrest and state of ill health. Galileo has become completely blind in 1636. This book was written in form of dialogues between three men e.g. Simplicio, Sagredo, and Salviati . The significance of this book can be realized form the fact that Galileo explained in it uniform velocity at page 128, acceleration at pages 133-134, 146, law of inertia at page 195 in section of The Motion Of Projectiles. Galileo’s this book deserves mention in the beginning due to reason the definitions of uniform velocity, acceleration and law of inertia are still used in the same form as given by Galileo. So much so Newton’s First Law of Motion is more refined form of Law of Inertia given by Galileo. The other book which has formed basis of physics and science is Newton’s Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy [1,2]) popularly known as the Principia. Newton initiated physics separating it from natural philosophy i.e. practically from zero state (that was genuine beginning of physics as subject). So he may be called originator of physics. The Principia was first published in Latin in 1686 and translated to English by Andrew Motte in 1729. In this book Newton had given new definitions, axioms or laws of motion and basics of law of gravitation. Between these two books (the Dialogue,1638 and the Principia,1686) French man Rene Descartes published Principles of Philosophy[4] 1644 , Christian Huygens, Horologium oscillatorium sive de motu pendularium [5] ,1673 ). All the interpretations are given in form of theorems, propositions etc. The concepts were justified geometrically and philosophically; not with mathematical equations. Likewise, Newton [1,2] did not give any mathematical equation in Mathematical Principles of Natural Philosophy, 1686 and explained phenomena geometrically and diagrammatically (simple, extremely speculative and complicated) without mathematical equations. Thus, geometry was the earliest method to interpret the perceptions. 1.2 Peculiarities of the Mathematical Principles of Natural Philosophy (Principia). Galileo has defined acceleration but did not apply acceleration in explaining motion of bodies as he applied uniform velocity in formulation of law of inertia. Galileo also defined uniform motion and applied the same in enunciation of Law of Inertia (1638). Descartes (1644) used the Law of Inertia in formulation of his second law of motion, and Huygens (1673) applied the same in formulation of his first hypothesis that bodies move with equal velocity in resistance free systems. Galileo (1638), Descartes (1644), Huygens (1673) did not use acceleration in explanation of motion of bodies. Also, Newton did not use acceleration purposely. Newton’s First Law of Motion is just other form of Law of Inertia. Newton improvised in Second Law of Motion by associating force with motion of bodies or changed kinematical system to dynamical system. Thus, Newton did not use acceleration in the Principia at all, even when he had opportunity to do so in the third and final edition of the Principia in 1727. Also, Newton did not write F =ma (Force = mass x acceleration), in his scientific career, as he did not write equation for acceleration. Galileo defined acceleration (dV/dt) in 1638 in the book Dialogue at page 133-134 and 146. Thus, acceleration was completely ignored by Newton as given 4 years before his death. In the discussion the scientific literature right from 1604 to 2011 is not only reviewed but critically analyzed impartially.
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