Newton's laws of motion

“ It is well known that the science of dynamics, as founded on Newton's laws of motion, does not supply any criterion by which rest may be distinguished from uniform motion; for if the laws of motion are applicable when the position of bodies is referred to any particular set of axes, they will be equally applicable when position is referred to any other set of axes which have a uniform motion of translation relative to these. ”

“ The reason is that the absolute theory of space is not really abandoned, and the relative motion, which is all that can be observed, is treated as the differential effect of two absolute motions.
8.5 In the enunciation of Newton's Laws of Motion, the velocities and accelerations of particles must be supposed to refer to the space of some given consentient set. Evidently the acceleration of a particle is the same in all the spaces of a simple group of consentient sets—at least this has hitherto been the unquestioned assumption. ”

“ Tait joins Sir W. Thomson in accepting, as bases for Physics, Newton's Laws of Motion? Though Newton gives illustrations of prolonged motion in bodies that are little resisted, he gives no proof that a body in motion will continue moving, if uninterfered with, in the same direction at the same velocity; nor, on turning to the enunciation of this law, quoted in the above-named work, do I find that Prof. Tait does more than exemplify it by facts which can themselves be asserted only by taking the law for granted. Does Prof. Tait deny that the first law of motion is a physical truth? ”

“ What force holds that moon forever circling about the earth? An apple falls to the ground beside him and its thud awakens a train of thought in his mind. Can it be the same force in the two cases—is the moon but a larger apple forever falling toward the earth, urged by the force of gravity, and forever receding from the earth, urged by her own uniform motion? Fascinated by the thought, Newton sets to calculating. He has studied out the laws of uniform motion and of accelerated motion—now he combines the two and gets the law of circular motion. ”

“ But by reason of the Tenacity of Fluids, and Attrition of their Parts, and the Weakness of Elasticity in Solids, Motion is much more apt to be lost than got, and is always upon the Decay. For Bodies which are either absolutely hard, or so soft as to be void of Elasticity, will not rebound from one another. Impenetrability makes them only stop. If two equal Bodies meet directly in vacuo, they will by the Laws of Motion stop where they meet, and lose all their Motion, and remain in rest, unless they be elastick, and receive new Motion from their Spring. ”

“ 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. ”

“ The relativity of motion is not emphasised so greatly204 in the Natural Philosophy as in some more modern treatises, but it is not overlooked; and whatever may be the view taken as to the importance of dwelling on such considerations in a treatise on dynamics, there can be no doubt that the return to Newton was on the whole a salutary change of the manner of teaching the subject.
The treatment of force in the first and second laws of motion is frankly causal. Force is there the cause of rate of change of momentum ”

“ The author was Albert Einstein, of Berne, Switzerland, a young man 376of twenty-six who had already made a number of notable contributions to theoretical physics.
The principle of relativity proposed by Einstein was by no means new to students of dynamics. Newton’s first two laws of motion express very clearly the fact that in mechanics all motion is relative. Force is proportional to acceleration, and the relation between the two is the same whether the motion under consideration is referred to fixed axes or to axes moving with a constant velocity. ”

“ It is true that metaphysicians hold that in the strictest sense absolute motion is not only unknowable but unthinkable, but we may say at least that the above method permits theoretically the detection of absolute translational motion in the same sense that a study of centrifugal forces enables us to detect absolute rotational motion. ”

“ 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 ”

“ 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. ”

“ 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 ”

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

“ 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, towards the contrary part. The changes made by these actions are equal, not in the velocities but in the motions of 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 towards contrary parts are reciprocally proportional to the bodies. ”

“ 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 ”

“ Now, from the law of conservation of momentum, A assumes that each ball experiences the same change in momentum, and therefore since he has already decided that the ball b has experienced a smaller change of velocity in the ratio , he must conclude that the mass of the ball in system b is greater than that of his own in the ratio .
In general, therefore, we must assume that the mass of a body increases with its velocity. We must bear in mind, however, as in all other cases, that the motion is determined with respect to some point arbitrarily chosen as a point of rest. ”

“ Every body perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed thereon. 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. ”

“ On similar grounds we may disprove the existence of any self-moving machine; for if it could once alter its own state of motion or rest, in however small a degree, there is no reason why it should not do the like time after time ad infinitum. Newton’s proof of his third law of motion, in the case of gravity, is of this character. For he remarks that if two gravitating bodies do not exert exactly equal forces in opposite directions, the one exerting the strongest pull will carry both away, and the two bodies will move off into space together with velocity increasing ad infinitum. ”

“ Therefore if a body projected from the place A in the direction of the right line AH, (Figure 6.) describes the Hyperbola AGK, and AH produced meets the asymptote NX in H, and AI drawn parallel to it meets the other asymptote MX in I; the density of the medium in A will be reciprocally as AH, and the velocity of the body as √AH2 / AI, and the resistance there to the force of gravity as AH to { (2nn + 2n) / (n + 2) } * AI. Hence the following rules are deduced. ”

“ 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 to treat of Mechanics is not my present business. I was only willing to show by those examples the great extent and certainty of the third Law of motion. For if we estimate the action of the agent from its force and velocity conjunctly; and likewise the reaction of the impediment conjunctly from the velocities of its several parts, and from the forces of resistance arising from the attrition, cohesion, weight, and acceleration of those parts; the action and re-action in the use of all sorts of Machines will be found always equal to one another. ”

“ When A is arrived at B, it cannot proceed farther without putting B into motion; and what motion it gives to B, it must lose it self, that the whole degree of motion of A and B together, if neither of the bodies be elastic, shall be equal, after the meeting of the bodies, to the single motion of A before the stroke. Therefore, from what has been said above, it is manifest, that as soon as the two bodies are met, they will move on together with a velocity, which will bear the same proportion to the original velocity of A, as the body A bears to the sum of both the bodies. ”

“ 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. ”

“ 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 ”

“ 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. ”

“ It is asserted, for instance, that acceleration must be relative since we measure it relatively to an inertial frame or to space. But here, of course, we have a mere confusion of words. The critic is assuming that absolute motion should mean motion with respect to nothing. But absolute motion in science does not mean this at all. It means motion which cannot be regarded as relative to something observable, such as matter; hence it becomes automatically motion with respect to something suprasensible, i.e., to space. ”

“ 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 acceleration of motion proportional thereto, as well in the parts of the machine as in the resisting body. ”