# Classical mechanics

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Diagram of orbital motion of a satellite around the earth, showing perpendicular velocity and acceleration (force) vectors.

Classical mechanics describes the motion of macroscopic objects, from projectiles to parts of machinery, as well as astronomical objects, such as spacecraft, planets, stars, and galaxies.

CONTENT : A - F , G - L , M - R , S - Z , See also , External links

## Quotes

Quotes are arranged alphabetically by author

### A - F

• In Newton's time only two kinds of force were available for quantitative investigation. One was the force of gravity; the other the forces of push and pull encountered in everyday life... Newton endeavored to construct a general theory of all forces, both those known in his time and those that might be discovered and investigated later. He intended his theory of gravitation to be one example that he himself could work out fully... Newton formulated his celebrated three laws: (1) In the absence of force, a body will continue at rest or in its present state of uniform rectilinear motion. (2) In the presence of force, a body will be accelerated in the direction of that force, the product of its mass by its acceleration being equal to the force (f = ma). (3) To every force there corresponds an equal counterforce, acting in a direction opposite to that of the force... According to the third law, then, each planet exerts an attractive counterforce to the sun, accelerating it toward the planet... a relatively small acceleration, because the mass of the sun so vastly exceeds... every planet...
• Peter G. Bergmann, The Riddle of Gravitation: From Newton to Einstein to Today's Exciting Theories (1968) pp. 13-14.
Niels Bohr & Albert Einstein at Paul Ehrenfest's home (1925)
• However far the phenomena transcend the scope of classical physical explanation, the account of all evidence must be expressed in classical terms. The argument is that simply by the word "experiment" we refer to a situation where we can tell others what we have done and what we have learned and that, therefore, the account of the experimental arrangement and of the results of the observations must be expressed in unambiguous language with suitable application of the terminology of classical physics.
• Niels Bohr, "Discussions with Einstein on Epistemological Problems in Atomic Physics," in Paul Arthur Schilpp, Albert Einstein: Philosopher Scientist (1949) pp. 199-241.
• A law explains a set of observations; a theory explains a set of laws. The quintessential illustration of this jump in level is the way in which Newton’s theory of mechanics explained Kepler’s law of planetary motion. Basically, a law applies to observed phenomena in one domain (e.g., planetary bodies and their movements), while a theory is intended to unify phenomena in many domains. Thus, Newton’s theory of mechanics explained not only Kepler’s laws, but also Galileo’s findings about the motion of balls rolling down an inclined plane, as well as the pattern of oceanic tides. Unlike laws, theories often postulate unobservable objects as part of their explanatory mechanism. So, for instance, Freud’s theory of mind relies upon the unobservable ego, superego, and id, and in modern physics we have theories of elementary particles that postulate various types of quarks, all of which have yet to be observed.
• John L. Casti in "Correlations, Causes, and Chance," Searching for Certainty: How Scientists Predict the Future (1990).
• From the thick darkness of the middle ages man's struggling spirit emerged as in new birth; breaking out of the iron control of that period; growing strong and confident in the tug and din of succeeding conflict and revolution, it bounded forwards and upwards with restless vigour to the investigation of physical and moral truth; ascending height after height; sweeping afar over the earth, penetrating afar up into the heavens; increasing in endeavour, enlarging in endowment; every where boldly, earnestly out-stretching, til, in the AUTHOR of the PRINCIPIA, one arose, who, grasping the master-key of the universe and treading its celestial paths, opened up to the human intellect the stupendous realities of the material world, and, in the unrolling of its harmonies, gave to the human heart a new song to the goodness, wisdom, and majesty of the all-creating, all-sustaining, all-perfect God.
• Newton then elevates this approximate empirical discovery to the position of a rigorous principle, the principle of inertia, and states that absolutely free bodies hence will cover equal distances in equal times. ...It is the principle of inertia coupled with an understanding of spatial congruence that yields us a definition of congruent stretches of absolute time. ...The principle of inertia, together with the other fundamental principles of mechanics, enables us... to place mechanics on a rigorous mathematical basis, and rational mechanics is the result. ...science, in the case of mechanics, has followed the same course as in geometry. Initially our information is empirical and suffers from all the inaccuracies ...But this empirical information is idealised, then crystallised into axioms, postulates or principles susceptible of direct mathematical treatment. ...If peradventure further experiment were to prove that our mathematical deductions ...were not born out in the world of reality, we should have to modify our initial principles and postulates or else agree that nature is irrational. With mechanics, the necessity of modifying the fundamental principles became imperative when it was recognized that the mass of a body was not the constant magnitude we thought it to be; hence it was experiment that brought about the revolution. On the other hand, in the case of geometry, it was the mathematicians themselves who forsaw the possibility of various non-Euclidean doctrines, prior to any suggestion of this sort being demanded by experiment.
• Although many historians of the new millennium now take issue with the notion of a Scientific Revolution, it is generally agreed that Newton's work culminated the long development of European science, creating a synthesis that opened the way for the scientific culture of the modern age.
• John Freely, Before Galileo: The Birth of Modern Science in Medieval Europe (2012)

### G - L

• I mentally conceive of some moveable [sphere] projected on a horizontal plane, all impediments being put aside. Now it is evident... that equable motion on this plane would be perpetual if the plane were of infinite extent, but if we assume it to be ended, and [situated] on high, the movable, driven to the end of this plane and going on further, adds on to its previous equable and indelible motion, that downward tendency which it has from its heaviness. Thus, there emerges a certain motion, compounded...
• On the authority of Aristotle... motion in the planetary world was somehow directed by the more perfect motion in higher spheres, and so on, up to the outermost sphere of fixed stars, indistinguishable from the prime mover. This implied a refined animistic and pantheistic world view, incomparably more rational than the ancient world views of Babylonians and Egyptians, among others, but a world view, nonetheless, hardly compatible with the idea of "inertial motion" which is implied in Buridan's concept of "impetus"… a momentous breaking point... which was to bear fruit... in the hands, first of Copernicus and then of Newton.
• Julio A. Gonzalo, The Intelligible Universe: An Overview of the Last Thirteen Billion Years (2008) 2nd edn.
• Wave functions, probabilities, quantum tunneling, the ceaseless roiling energy fluctuations of the vacuum, the smearing together of space and time, the relative nature of simultaneity, the warping of the spacetime fabric, black holes, the big bang. Who could have guessed that the intuitive, mechanical, clockwork Newtonian perspective would turn out to be so thoroughly parachial—that there would be a whole new mind-boggling world lying just beneath the surface of things as they are ordinarily experienced?
• Brian Greene, The Elegant Universe (1999, 2003) Ch. 15 "Prospects."
• Newton's system was for a long time considered as final and the task... seemed simply to be an expansion.... From the theory of the motion of mass points one could go over to the mechanics of solid bodies, to rotatory motions, and one could treat the continuous motion of fluid or the vibrating motion of an elastic body. All these... were gradually developed... with the evolution of mathematics, especially of the differential calculus... checked by experiments. Acoustics and hydrodynamics became a part of mechanics. Another science... was astronomy. Improvements... led to... more accurate determinations of the motions of the planets... When the phenomena of electricity and magnetism were discovered, the... forces were compared to the gravitational forces... Finally, in the nineteenth century, even the theory of heat could be reduced...
• The first difficulty arose in the discussion of the electromagnetic field in... Faraday and Maxwell. In Newtonian mechanics the gravitational force had been considered as given... In the work of Faraday and Maxwell... the field of force... became the object of the investigation... they tried to set up equations of motion for the fields, not primarily for the bodies... This change led back to a point of view...held... before Newton. An action could... be transferred... only when the two bodies touched... Newton had introduce a very new and strange hypothesis by assuming a force that acted over a long distance. Now in the theory of fields... action is transferred from one point to a neighboring point... in terms of differential equations. ...the description of the electromagnetic fields... by Maxwell's equations seemed a satisfactory solution of the problem of force. ...The axioms and definitions of Newton had referred to bodies and their motion; but with Maxwell the fields... seemed to have acquired the same degree of reality as the bodies in Newton's theory. This view... was not easily accepted; and to avoid such a change in the concept of reality... many physicists believed that Maxwell's equations actually referred to the deformations of an elastic medium... the ether... the medium was so light and thin that it could penetrate into other matter and could not be seen or felt. ...[H]owever ...it could not explain the complete absence of any longitudinal light waves.
• I shall try to sum up the main obstacles which arrested the progress of science for such an immeasurable time. The first was the splitting of the world into two spheres, and the mental split which resulted from it. The second was the geocentric dogma, the blind eye turned on the promising line of thought which had started with the Pythagoreans and stopped abruptly with Aristarchus of Samos. The third was the dogma of uniform motion in perfect circles. The fourth was the divorcement of science from mathematics. The fifth was the inability to realize that a body at rest tended to stay at rest, a body in motion tended to stay in motion. The main achievement of the first part of the scientific revolution was the removal of these five cardinal obstacles. This was done chiefly by three men: Copernicus, Kepler and Galileo. After that, the road was open to the Newtonian synthesis; from there on the journey led with rapidly gaining speed to the atomic age.

### M - R

• The history of the development of mechanics is quite indispensable to a full comprehension of the science in its present condition. It also affords a simple and instructive example of the processes by which natural science generally is developed.
• Ernst Mach, The Science of Mechanics: A Critical and Historical Account of Its Development (1893,1960) Tr. Thomas J. McCormack.
• These independent objects of Newtonian physics might move, touch each other, collide, or even, by a certain stretch of the imagination, act at a distance: but nothing could penetrate them except in the limited way that light penetrated translucent substances. This world of separate bodies, unaffected by the accidents of history or geographic location, underwent a profound change with the elaboration of the new concepts of matter and energy that went forward from Faraday and von Mayer through Clerk-Maxwell and Willard Gibbs and Ernest Mach to Planck and Einstein. The discovery that solids, liquids, and gases were phases of all forms of matter modified the very conceptions of substance, while the identification of electricity, light, and heat as aspects of a protean energy, and the final break-up of "solid" matter into particles of this same ultimate energy lessened the gap, not merely between various aspects of the physical world, but between the mechanical and the organic. Both matter in the raw and the more organized and internally self-sustaining organisms could be described as systems of energy in more or less stable, more or less complex, states of equilibrium.
• Lewis Mumford, Technics and Civilization (1934) Ch.8 "Orientation"
• Galileo's comprehension of the concept of acceleration, which he defined as a change of velocity either in magnitude or direction... was an abstract idea that no one seems to have thought much about before. And in using it to test the still accepted Aristotelian precept that a moving object requires a force to maintain it, Galileo easily demonstrated that it is not motion but rather acceleration which cannot occur without an external force. Deliberately rejecting common sense as a prejudiced witness, he let nature herself speak in the form of a "hard, smooth and very round ball" rolling down a "very straight" ideal groove lined with polished parchment, and then rolling up another groove, clocking each roll "hundreds or times"... he showed that, while downward motion (helped by gravity force) makes speed increase and upward motion (hindered by gravity force) makes speed decrease, there is always a "boundary case" in between... where speed remains constant (without any appreciable force)—and that, by reducing friction, this boundary case can be made to approach a horizontal level where gravity has no effect. Similarly testing... he also drafted a law of falling bodies: "that the distances traversed, during equal intervals of time... stand to one another in the same ratio as the odd numbers beginning with unity." And his beautiful analysis of a cannonball's trajectory into horizontal and vertical components... was one day to be of enormous help to Isaac Newton in solving the riddle of gravity.

### S - Z

• Newton proposed that the particles of the air (we would call them molecules), were motionless in space and were held apart by repulsive forces between them... He assumed that the repulsive force was inversely proportional to the distance between the particles...He showed that, on the basis of this assumption, a collection of static particles in a box would behave exactly as Boyle had found. His model led directly to Boyle's law. Probably the greatest scientist ever, Newton managed to get the right answer from a model that was wrong in every possible way.
• Brian L. Silver, The Ascent of Science (1998)
• The founders of modern science - for instance, Galileo, Kepler, and Newton - were mostly pious men who did not doubt God’s purposes. Nevertheless they took the revolutionary step of consciously and deliberately expelling the idea of purpose as controlling nature from their new science of nature. They did this on the ground that inquiry into purposes is useless for what science aims at: namely, the prediction and control of events. To predict an eclipse, what you have to know is not its purpose but its causes. Hence science from the seventeenth century onwards became exclusively an inquiry into causes. The conception of purpose in the world was ignored and frowned on. This, though silent and almost unnoticed, was the greatest revolution in human history, far outweighing in importance any of the political revolutions whose thunder has reverberated through the world.
• Newton did not show the cause of the apple falling, but he shewed a similitude between the apple and the stars. By doing so he turned old facts into new knowledge; and was well content if he could bring diverse phenomenon under "two or three Principles of Motion" even "though the Causes of these Principles were not yet discovered."
• Newtonian mechanics does not apply to all situations. If the speeds of the interacting bodies are very large —an appreciable fraction of the speed of light —we must replace Newtonian mechanics with Einstein’s special theory of relativity, which holds at any speed, including those near the speed of light. If the interacting bodies are on the scale of atomic structure (for example, they might be electrons in an atom), we must replace Newtonian mechanics with quantum mechanics. Physicists now view Newtonian mechanics as a special case of these two more comprehensive theories. Still, it is a very important special case because it applies to the motion of objects ranging in size from the very small (almost on the scale of atomic structure) to astronomical (galaxies and clusters of galaxies).
• Jearl Walker, David Halliday, and Robert Resnick, Fundamentals of physics (10th ed., 2014), Ch. 5 : Force and Motion—I
• The foundational achievement of classical mechanics is to establish that the first point is faulty. It is fruitful, in that framework, to allow a broader concept of the character of physical reality. To know the state of a system of particles, one must know not only their positions, but also their velocities and their masses. Armed with that information, classical mechanics predicts the system’s future evolution completely. Classical mechanics, given its broader concept of physical reality, is the very model of Einstein Sanity.