ESA Science - Newton In Space (Part 2): Newton's Second Law of Motion - Force, Mass And Acceleration.
Newton's laws of motion are three physical laws that form the basis for classical mechanics. They have been expressed in several different ways over nearly three centuries.
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The laws describe the relationship between the forces acting on a body and the motion of that body. They were first compiled by Sir Isaac Newton in his work "Philosophiæ Naturalis Principia Mathematica", first published on July 5, 1687.
Newton used them to explain and investigate the motion of many physical objects and systems. For example, in the third volume of the text, Newton showed that these laws of motion, combined with his law of universal gravitation, explained Kepler's laws of planetary motion.
Newton's Second Law of Motion: A body will accelerate with acceleration proportional to the force and inversely proportional to the mass.
Observed from an inertial reference frame, the net force on a particle is equal to the time rate of change of its linear momentum: F = d(mv)/dt. Since by definition the mass of a particle is constant, this law is often stated as, "Force equals mass times acceleration (F = ma): the net force on an object is equal to the mass of the object multiplied by its acceleration."
History of the second law
Newton's Latin wording for the second law is: "Lex II: Mutationem motus proportionalem esse vi motrici impressae, et fieri secundum lineam rectam qua vis illa imprimitur."
This was translated quite closely in Motte's 1729 translation as: "LAW II: The alteration of motion is ever proportional to the motive force impress'd; and is made in the direction of the right line in which that force is impress'd."
According to modern ideas of how Newton was using his terminology, this is understood, in modern terms, as an equivalent of: "The change of momentum of a body is proportional to the impulse impressed on the body, and happens along the straight line on which that impulse is impressed."
Motte's 1729 translation of Newton's Latin continued with Newton's commentary on the second law of motion, reading: "If a force generates a motion, a double force will generate double the motion, a triple force triple the motion, whether that force be impressed altogether and at once, or gradually and successively. And this motion (being always directed the same way with the generating force), if the body moved before, is added to or subtracted from the former motion, according as they directly conspire with or are directly contrary to each other; or obliquely joined, when they are oblique, so as to produce a new motion compounded from the determination of both."
The sense or senses in which Newton used his terminology, and how he understood the second law and intended it to be understood, have been extensively discussed by historians of science, along with the relations between Newton's formulation and modern formulations.