Newton's laws of motion: Encyclopedia II - Newton's laws of motion - Newton's second law - historical development

Newton's laws of motion - Newton's second law - historical development

In an exact original 1792 translation (from Latin) Newton's Second Law of Motion reads:

"LAW II: The alteration of motion is ever proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed. -- 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."

Newton here is basically saying that the change in the momentum of an object is proportional to the amount of force exerted upon the object. He also states that the change in direction of momentum is determined by the angle from which the force is applied. Interestingly, Newton is restating in his further explanation another prior idea of Galileo being what we call today the Galilean transformation or the addition of velocities.

An interesting fact when studying Newton's Laws of Motion from the Principia is that Newton himself does not explicitly write formulae for his laws which was common in scientific writings of that time period. In fact, it is today commonly added when stating Newton's second law that Newton has said, "and inversely proportional to the mass of the object." This however is not found in Newton's second law as directly translated above. In fact, the idea of mass is not introduced until the third law. However, it has been a common convention to describe law two of Newton in the mathematical formula F=ma where F is Force, a is acceleration and m is mass. This is actually a combination of laws two and three of Newton expressed in a very useful form. This formula in this form did not even begin to be used until the 18th century after Newton's death, but it is implicit in his laws.

Newton's Third Law of Motion states: "LAW III: To every action there is always opposed an equal reaction: or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts. -- Whatever draws or presses another is as much drawn or pressed by that other. If you press a stone with your finger, the finger is also pressed by the stone. If a horse draws a stone tied to a rope, the horse (if I may so say) will be equally drawn back towards the stone: for the distended rope, by the same endeavour to relax or unbend itself, will draw the horse as much towards the stone, as it does the stone towards the horse, and will obstruct the progress of the one as much as it advances that of the other. If a body impinge upon another, and by its force change the motion of the other, that body also (because of the equality of the mutual pressure) will undergo an equal change, in its own motion, toward the contrary part. The changes made by these actions are equal, not in the velocities but in the motions of the bodies; that is to say, if the bodies are not hindered by any other impediments. For, because the motions are equally changed, the changes of the velocities made toward contrary parts are reciprocally proportional to the bodies. This law takes place also in attractions, as will be proved in the next scholium."

The explanation of mass is expressed here for the first time in the words "reciprocally proportional to the bodies" which have now been traditionally added to Law 2 as "inversely proportional to the mass of the object." This is because Newton in his definition 1 had already stated that when he said "body" he meant "mass". Thus we arrive at F=ma.

Adapted from the Wikipedia article "Newton's second law - historical development", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki