Momentum

“ Of the two endowments of energy and of moment of momentum originally conferred on our system the moment of momentum is the entailed estate. No matter how the bodies may move, no matter how their actions may interfere with one another, no matter how this body is pulled one way and the other body that way, the conservation of moment of momentum is not imperilled, nor, no matter what losses of heat may be experienced by radiation, could the store of moment of momentum be affected. ”

“ In like manner, we see bodies striking each other, and thus moving and stopping, accelerating and retarding each other: but in all this, we do not perceive by our senses that abstract quantity, Momentum, which is always lost by one body as it is gained by another. This Momentum is a creation of the mind, brought in among the facts, in order to convert their apparent confusion into order, their seeming chance into certainty, their perplexing variety into simplicity. ”

“ Remarks.—As the ubication, so also the momentum produced by accidental action, can be considered both absolutely and respectively. The momentum, considered absolutely, is an act received in a subject—an absolute momentum, an extrinsic term of the virtuality of the motive principle; and, as such a momentum is only one out of the innumerable acts which can proceed from the agent, it has an entity infinitely less than that of the agent. ”

“ Hence we may conclude that every such system as is presented to us in the infinite variety of Nature, must stand in intimate relation to some particular plane, being that which is known as the principal plane of moment of momentum. ”

“ We realize with difficulty the momentum (giving to this word the meaning usually assigned to it by physicists) of a new idea, which leads in its train a veritable world and pushes another on before it. ”

“ The force is mass I think he said the force, Times acceleration. I know that word, of course, Yes, the force is the mass It's all becoming clear, Times the acceleration, or more precisely, the time derivative of the linear momentum. ”

“ But from the expression for the moment of momentum we see that this is greatest when e is least. If, therefore, a is diminished, e must also be diminished, or the moment of momentum would be lessened, which is impossible. ”

“ Momentum in physics, if properly directed, will drive a tallow candle through an inch board. Just so will oneness of aim and the direction of the energies to a single pursuit, while all others are waived, enable the veriest weakling to make his mark where he strikes. The general who scatters his soldiers all about the country insures defeat; so does he whose attention is diffused through innumerable channels, so that it can not gather in force on {154} any one point. The human mind, in short, resembles a burning-glass, whose rays are intense only as they are concentrated. ”

“ With increased momentum you get an increased rate as multiplied by space. I am not an expert, but this is practically true. In the same way, spiritual perception acts with increased momentum.
All sin is failure in spiritual perception. Spiritual perception corresponds with the momentum of a falling body in mechanics. Only in Divine mechanics it is a rising body ”

“ It is the force, or power, with which a body in motion, strikes against another body. The momentum of a body is the product of its quantity of matter, multiplied by its quantity of motion; in other words, its weight multiplied by its velocity. ”

“ According to modern definition, tangential momentum is not, properly speaking, a Force.
"Let knowledge grow from more to more, yet more of reverence in us dwell;" reverence for the Light vouchsafed to those who had not our advantages in the way of technical knowledge. ”

“ The only ray of hope was to be found in the deficiency in one of the two great requisites of such a force. Momentum being weight, multiplied into velocity, there were some glimpses visible, of a nature to produce a slight degree of expectation that the last might yet be resisted. ”

“ MECHANICS.—The whole momentum or quantity of force of a moving body, is the result of the quantity of matter, multiplied by the velocity with which it is moved; and when the product arising from the multiplication of the particular quantities of matter in any two bodies, by their respective velocities are equal, their momentum will be so too. ”

“ In the production of motion by force, for instance, though the effect be cumulative with continued exertion of the cause, yet each elementary or individual action is, to our apprehension, instanter accompanied with its corresponding increment of momentum in the body moved. In all dynamical 195 reasonings no one has ever thought of interposing an instant of time between the action and its resulting momentum ”

“ In the proof thus added, ‘We are agreed,’ says the interlocutor31, ‘that in a moving body the impetus, energy, momentum, or propension to motion, is as great as is the force or least resistance which suffices to sustain it;’ and the impetus or momentum, in the course of the proof, being taken to be as the velocity produced in a given time, it is manifest that the principle so stated amounts to this; that the velocity produced is as the statical force. ”

“ It is sufficient for the purpose of a perpetual motion that they can do this. And, indeed, here all the difficulty lies, viz., in the means of communicating the momentum or moving force of a heavy body to a light one. Now, the most virulent opponents to the practicability of perpetual motion have never pretended to demonstrate the impracticability of this communication.235 The quomodo, or means of effecting it, being the point in dispute. ”

“ Caroline. The quicker a body moves, the greater, no doubt, must be the force which it would strike against another body.
Emily. Therefore a light body may have a greater momentum than a heavier one, provided its velocity be sufficiently increased; for instance, the momentum of an arrow shot from a bow, must be greater than that of a stone thrown by the hand. ”

“ Every such action must be composed of the effects of one particle in the system on another, and as this must invariably produce an equal and opposite reaction the total moment of momentum is unaltered. ”

“ Hence it is clear that equal spaces will be traversed in equal times by two bodies, one of which, starting from rest, moves with a uniform acceleration, while the momentum of the other, moving with uniform speed, is one-half its maximum momentum under accelerated motion. ”

“ A knowledge of the mobility of the molecules of water, of the rotation of the earth, of temperature, of the action of the moon and the sun, of the contour of coasts, of the deflection of currents, of the curvature of the earth, of the principles of momentum, and the like, is the means of perceiving the causes of currents. In the degree that the causes are explained we have the philosophy of currents. ”

“ We choose any point O in the plane, and for simplicity we have so drawn the figure that A, B, and C are forces tending to turn round O in the same direction. The velocity of a body multiplied into its mass is termed the momentum of the body. ”

“ The momentum is considered respectively when it is compared with another momentum, in which case we can find the relation of the one to the other as to intensity. This intensity is measured by the quantity of the movement to which [388] they give rise when not counteracted. ”

“ Let us suppose the earth, of given weight, moving with given momentum in a given path, and under given conditions in every respect, to find itself at any one time conditioned in all these respects as it was conditioned at some past moment ”

“ According to him, force is merely rate of change of momentum. Hence the forces in equations of motion are only expressions, the values of which as rates of change of momentum, are to be made explicit by the solution of such equations in terms of known quantities. ”

“ The third law of motion tells us that action and reaction are equal and opposite, so that when two bodies come into collision the forces at work generate equal and opposite quantities of momentum. We shall best see the meaning of this law by a numerical example, bearing in mind that momentum means the product of mass into velocity. ”

“ I am one of those who accept the proposition, and believe that a falling body acquires force [vires] in its descent, its velocity increasing in proportion to the space, and that the momentum [momento] of the falling body is doubled when it falls from a doubled height ”

“ The resurrection of the dead is a stupendous work of God; it requires his might in sovereign action; and when we consider that all mankind are to be raised and changed in a moment, in the twinkling of an eye, then the momentum, or velocity, with which the power is to be applied must be inconceivably great. All motion is in proportion to the quantity of matter in the mover, and the velocity with which it is applied. ”

“ In the case of a connected system in motion, the configuration is continually changing at a rate depending on the velocities so that we can no longer assume that the momentum is the time-integral of the force which acts on it. ”

“ Energy momentum and stress, which we have identified with the ten principal curvatures of the world, are the subject of the famous laws of conservation of energy and momentum. Granting that the identification is correct, these laws are mathematical identities. Violation of them is unthinkable. Perhaps I can best indicate their nature by an analogy. ”

“ It will thus be seen that Momentum and Energy are entirely different, although co-related; that momentum relates to velocity, which includes the element of time, whereas energy relates211 to the amount of work done, and may be represented by a force operating against a certain resistance, through a certain distance, entirely irrespective of time. The energy is the same with the same force operating against the same resistance, through the same distance whether the time consumed be great or small. ”

“ Professor Archimedes would be explaining the theory that, if a force act upon a body, the measure of the force in absolute units is numerically equal to the time-rate of change of momentum and to the space-rate of change of kinetic energy ”

“ Falling bodies afford the most perfect illustration of the principle of Momentum and Energy, and are so commonly used to illustrate those principles that many students get the idea that the application of those principles is confined to falling bodies, and do not realize that they extend generally through the field of mechanics. ”

“ In problems of impact we have to deal with cases of practically instantaneous impulse, where a very great and rapidly varying force produces an appreciable change of momentum in an exceedingly minute interval of time. ”

“ Transformation of momentum, energy and stresses. The transformation formulas for momentum, energy density and the stresses in the passage from one valid reference system to another system , is definitely determined by deriving them from the components of the world tensor . ”

“ II. The general proposition that when once a cause is removed its effect vanishes, is not universally applicable. Take, for instance, the following example:—if you once communicate a certain amount of momentum to a ball, velocity of a particular degree in a particular direction is the result. ”

“ Let us suppose that the mass acted on per second be divided into parts, and that each part be acted on by the force for th of a second. Then the momentum communicated to each part and the total momentum per second which holds good when the number of parts becomes infinite and the communication of momentum continuous. ”

“ The mind of the narrator, like the stone descending the shaft, gathers accelerated velocity with its momentum toward the last, and so expends itself in a more brief and sententious manner than in the commencement. ”

“ Reverting to the case of a body supported by the communication of momentum to a number of independent material particles, it is evident that the particles projected downwards eventually give up their momentum on striking the surface of the earth. ”

“ The part with which the striking body comes in contact, receiving the whole of the communicated momentum, is driven in towards the centre of the mass. It thus compresses and tends to displace the more centrally situated portions of the mass. ”

“ This can be proved, since, if the impetus carries a moving body with a momentum equal to 4 and the moving body wants to turn and fall back with a momentum of 4, then one momentum neutralises the other contrary one, and the impetus is neutralised. ”