Newton's third law of motion

“ And therefore the parts equally press each other by their weights, that is, equally attract each other, according to the third Law of Motion; and, if separated and let go, would fall towards each other with velocities reciprocally as the bodies. All which we may try and see in the load-stone, whose attracted part does not propel the part attracting, but is only stopped and sustained thereby. ”

“ A further principle of great importance, of which only very indistinct traces are to be found before Newton's time, was given by him as the Third Law of Motion in the form: "To every action there is always an equal and contrary reaction ”

“ Newton's first law teaches that a body, once set in motion, will continue to move on with uniform velocity in a straight line forever if left to itself. To produce circular motion a constant force directed toward a fixed point must be applied in addition to the original force. The fixed point then becomes the centre of revolution. ”

“ As MacLaurin points out, the Third Law of Motion may be extended to all sorts of powers that take place in Nature, and belongs to attraction and repulsion of all kinds, and must not be considered as being arbitrarily introduced by Newton. ”

“ True motion is neither generated nor alter'd, but by some force impress'd upon the body moved: but relative motion may be generated or alter'd without any force impress'd upon the body. For it is sufficient only to impress some force on other bodies with which the former is compar'd, that by their giving way, that relation may be chang'd, in which the relative rest or motion of this other body did consist. Again, True motion suffers always some change from any force impress'd upon the moving body ”

“ We may also mention that the very possibility of there being definite laws of mechanics, such as the law of inertia, is contingent upon the existence of certain fundamental differences between the various frames. If all frames were identical, as the complete relativity of motion would demand, the law of inertia would express nothing at all. In every case we might make the motion of a body appear anything we wished by selecting our frame suitably; and if we had no means of distinguishing one frame from another the straight path of a body through empty space would convey no physical meaning. ”

“ If the action of the circum-terrestrial force is proportional to the bodies to be moved, it will (by the Second Law of Motion) move them with equal velocity in equal times, and will make all bodies let fall to descend through equal spaces in equal times, and all bodies hung by equal threads to vibrate in equal times. If the action of the force was greater, the times would be less ”

“ Newton’s Second Law asserts that change of momentum is equal to the impulse; this is a statement as to equality of vectors and so implies identity of direction as well as of magnitude. If X, Y, Z are the components of force, then considering the changes in an infinitely short time δt we have, by projection on the co-ordinate axes, δ (mu) = Xδt, and so on, or
(2)
For example, the path of a particle projected anyhow under gravity will obviously be confined to the vertical plane through the initial direction of motion. ”

“ The fundamental hypothesis of the science assumes a system of bodies in motion, of which the sun and planets may be taken as examples, and of which each separate body is attracted toward all the others according to the law of Newton. The motion of each body is then expressed in the first place by Newton’s three laws of motion (see Motion, Laws of, and Mechanics) . ”

“ The quantity of motion, which is collected by taking the sum of the motions directed towards the same parts, and the difference of those that are directed to contrary parts, suffers no change from the action of bodies among themselves. For Action and its opposite Re-action are equal, by Law 3, and therefore, by Law 2, they produce in the motions equal changes towards opposite parts. Therefore if the motions are directed towards the same parts, whatever is added to the motion of the preceding body will be subducted from the motion of that which follows ”

“ And since similar, equal, and equally swift bodies, moving through mediums of the same density, whose particles do not fly from each other mutually, will strike against an equal quantity of matter in equal times, whether the particles of which the medium consists be more and smaller, or fewer and greater, and therefore impress on that matter an equal quantity of motion, and in return (by the 3d Law of Motion) suffer an equal re-action from the same, that is, are equally resisted ”

“ But I shall now pass to the second law of motion; wherein, when it is asserted, that the velocity, with which any body is moved by the action of a power upon it, is proportional to that power; the degree of power is supposed to be measured by the greatness of the body, which it can move with a given celerity. So that the sense of this law is, that if any body were put into motion with that degree of swiftness, as to pass in one hour the length of a thousand yards ”

“ I have hitherto been treating of the attractions of bodies towards an immovable centre; though very probably there is no such thing existent in nature. For attractions are made towards bodies, and the actions of the bodies attracted and attracting are always reciprocal and equal, by Law III; so that if there are two bodies, neither the attracted nor the attracting body is truly at rest, but both (by Cor. 4, of the Laws of Motion) , being as it were mutually attracted, revolve about a common centre of gravity. ”

“ By this Principle alone there never could have been any Motion in the World. Some other Principle was necessary for putting Bodies into Motion; and now they are in Motion, some other Principle is necessary for conserving the Motion. For from the various Composition of two Motions, 'tis very certain that there is not always the same quantity of Motion in the World. For if two Globes joined by a slender Rod, revolve about their common Center of Gravity with an uniform Motion, while that Center moves on uniformly in a right Line drawn in the Plane of their circular Motion ”

“ If a body is resisted in the ratio of its velocity, the motion lost by resistance is as the space gone over in its motion.
or since the motion lost in each equal particle of time is as the velocity, that is, as the particle of space gone over; thesis by composition, the motion lost in the whole time will be as the whole space gone over. Q.E.D.
Corollary. Therefore if the body, destitute of all gravity, move by its innate force only in free spaces, and there be given both its whole motion at the beginning, and also the motion remaining after some part of the way is gone over ”

“ Therefore if we suppose two systems of this kind, the correspondent particles, by reason of the similitude of the motions at their beginning, will continue to be moved with like motions, so long as they move without meeting one another. For if they are acted on by no forces, they will go on uniformly in right lines by the 1st law. But if they do agitate one another, with some certain forces, and those forces are as the diameters of the correspondent particles inversely and the squares of the velocities directly ”

“ PRojectiles persevere in their motions, so far as they are not retarded by the resistance of the air, or impelled downwards by the force of gravity. A top, whose parts by their cohesion are perpetually drawn aside from rectilinear motions, does not cease its rotation, otherwise than as it is retarded by the air. The greater bodies of the planets and comets, meeting with less resistance in more free spaces, preserve the motions both progressive and circular for a much longer time.
Law II.
The alteration of motion is ever proportional to the motive force impress'd ”

“ The theory of the rotation of a rigid system is strictly deduced from the elementary laws of motion, but the complexity of the motion of the particles of a body freely rotating renders the subject so intricate, that it has never been thoroughly understood by any but the most expert mathematicians. Many who have mastered the lunar theory have come to erroneous conclusions on this subject; and even Newton has chosen to deduce the disturbance of the earth’s axis from his theory of the motion of the nodes of a free orbit, rather than attack the problem of the rotation of a solid body. ”

“ It would appear, then, to be more correct to state that there can exist no such thing as freely moving bodies, since all bodies are subjected to the influence of the guiding field. We can, however, retain the usual terminology by remembering that by a freely moving body we mean one submitted to the action of the guiding field and to nothing else. The important point to understand is that as regards freedom of motion, all bodies in empty space, whether situated in a gravitational field or far from matter, are on the same footing. ”

“ Therefore, a homogeneous and perfect globe will not retain several distinct motions, but will unite all those that are impressed on it, and reduce them into one; revolving, as far as in it lies, always with a simple and uniform motion about one single given axis, with an inclination perpetually invariable. And the inclination of the axis, or the velocity of the rotation, will not be changed by centripetal force. ”

“ Let the times be expounded by T and t, and the velocities by GH/T and HI/t, and the decrement of the velocity produced in the time t will be expounded by GH/T - HI/t. This decrement arises from the resistance which retards the body, and from the gravity which accelerates it. Gravity, in a falling body, which in its fall describes the space NI, produces a velocity, with which it would be able to describe twice that space in the same time, as Galileo has demonstrated ”

“ For all the parts of revolving bodies endeavour to recede from the axis of motion; and the impetus of bodies moving forward, arises from the joint impetus of all the parts. Therefore, if surrounding bodies are moved, those that are relatively at rest within them, will partake of their motion. Upon which account, the true and absolute motion of a body cannot be determined by the translation of it from those which only seem to rest; for the external bodies ought not only to appear at rest, but to be really at rest. ”

“ It has been demonstrated by science that motion is persistent—cannot be created or annihilated—and the demonstration has been accepted by a great body of scientific men. Antecedently to this demonstration Newton had propounded three laws of motion, one of which is that action and reaction are equal and in opposite directions. In this law the persistence of motion or the indestructibility of energy was implied, but at first its full significance was not understood, perhaps not even by Newton himself. ”

“ So that if the disparity of velocities is so great as to overcome all that resistance which commonly arises either from the attrition of contiguous bodies as they slide by one another, or from the cohesion of continuous bodies that are to be separated, or from the weights of bodies to be raised, the excess of the force remaining, after all those resistances are overcome, will produce an acceleration of motion proportional thereto, as well in the parts of the machine as in the resisting body. ”