The Generalized Form of Principia’s Third Law of Motion

Objective: Third law is critically analysed in view of definition and elaboration given by Newton at page 20 of the Principia. It is evident that law is incompletely studied. Methods/Analysis: Newton did not give any mathematical equation for the law. The definition and explanation of the law is completely analyzed theoretically and discussed in view of the experimental data. Newton’s explanation is simply qualitative, not quantitative which is required for scientific analysis. The law is universally applicable to all cases and all bodies without any constraint. However Newton elaborated the same in terms of just three qualitative examples which is not scientific. Findings: The terms action and reaction neither possess units nor dimensions, even expressed in terms of equations the explanation is qualitative only. The law is understood in terms of force only. However Newton expressed law in terms of both force and velocity in three examples. If law is expressed in terms of force and velocity analogous to action and reaction, then its limitations are evident. For example it does not account for the significant factors e.g. inherent characteristics, nature, compositions, flexibility, rigidity, magnitude, size, elasticity, shape, distinctiveness of interacting bodies, mode of interactions, point of impact etc. The law is universally applicable for all bodies e.g. bodies may be of steel, wood, rubber, cloth, wool, sponge, spring, typical plastic, porous material, air/fluid filled artifact, mud or kneaded flour or chewing gum specifically fabricated material etc. For all such bodies if the action is same, then the reaction must be the same. But it is not found true in all cases, as interaction between rubber and steel are different from rubber and cotton. Application/Improvements: Thus law is generalized; reaction is proportional to action depending upon characteristics of system. Mathematically, Reaction = -K action, the value of K may be equal to, less than, or greater than unity depending upon experimental parameters.