Centrifugal Families Are More _____ Than Centripetal Families.

In physics, the history of centrifugal and centripetal forces illustrates a long and complex evolution of idea about the nature of forces, relativity, and the nature of physical laws.

Huygens, Leibniz, Newton, and Hooke [edit]

Early scientific ideas about centrifugal force were based upon intuitive perception, and circular motion was considered somehow more "natural" than straight-line motion. According to Domenico Bertoloni-Meli:

For Huygens and Newton centrifugal force was the result of a curvilinear motion of a body; hence it was located in nature, in the object of investigation. According to a more recent conception of classical mechanics, centrifugal force depends on the choice of how phenomena tin can be conveniently represented. Hence information technology is not located in nature, but is the event of a choice by the observer. In the first example a mathematical conception mirrors centrifugal force; in the second it creates it.^[1]

Christiaan Huygens coined the term "centrifugal force" in his 1659 De Vi Centrifuga ^[2] and wrote of it in his 1673 Horologium Oscillatorium on pendulums. In 1676–77, Isaac Newton combined Kepler's laws of planetary movement with Huygens' ideas and constitute

the proffer that by a centrifugal force reciprocally equally the square of the distance a planet must circumduct in an ellipsis about the center of the forcefulness placed in the lower omphalus of the ellipsis, and with a radius drawn to that center, describe areas proportional to the times.^[3]

Newton coined the term "centripetal force" (vis centripeta) in his discussions of gravity in his De motu corporum in gyrum, a 1684 manuscript which he sent to Edmond Halley.^[iv]

Gottfried Leibniz as part of his "solar vortex theory" conceived of centrifugal strength every bit a real outward force which is induced by the apportionment of the trunk upon which the force acts. An inverse cube police centrifugal force appears in an equation representing planetary orbits, including non-circular ones, every bit Leibniz described in his 1689 Tentamen de motuum coelestium causis.^[v] Leibniz'due south equation is withal used today to solve planetary orbital problems, although his solar vortex theory is no longer used as its basis.^[6]

Leibniz produced an equation for planetary orbits in which the centrifugal force appeared as an outward inverse cube law force in the radial management:^[7]

${\displaystyle {\ddot {r}}=-yard/r^{2}+l^{2}/r^{3}}$ .

Newton himself appears to accept previously supported an approach like to that of Leibniz.^[eight] Later, Newton in his Principia crucially limited the description of the dynamics of planetary motion to a frame of reference in which the point of allure is fixed. In this description, Leibniz's centrifugal force was not needed and was replaced by only continually inward forces toward the fixed signal.^[7] Newton objected to Leibniz's equation on the grounds that it allowed for the centrifugal force to have a different value from the centripetal force, arguing on the basis of his 3rd law of motion, that the centrifugal force and the centripetal force must constitute an equal and opposite action-reaction pair. In this however, Newton was mistaken, every bit the reactive centrifugal strength which is required by the third law of motion is a completely separate concept from the centrifugal forcefulness of Leibniz's equation.^{[8] [9]}

Huygens, who was, along with Leibniz, a neo-Cartesian and critic of Newton, ended afterward a long correspondence that Leibniz's writings on celestial mechanics made no sense, and that his invocation of a harmonic vortex was logically redundant, because Leibniz'southward radial equation of motion follows trivially from Newton's laws. Fifty-fifty the most ardent modern defenders of the cogency of Leibniz's ideas admit that his harmonic vortex equally the basis of centrifugal force was dynamically superfluous.^[x]

Information technology has been suggested that the idea of circular motion as caused by a single force was introduced to Newton by Robert Hooke.^[9]

Newton described the office of centrifugal force upon the height of the oceans near the equator in the Principia:

Since the centrifugal force of the parts of the earth, arising from the earth's diurnal motion, which is to the forcefulness of gravity equally one to 289, raises the waters under the equator to a elevation exceeding that under the poles past 85472 Paris feet, as in a higher place, in Prop. XIX., the force of the sun, which we have at present shewed to be to the forcefulness of gravity as ane to 12868200, and therefore is to that centrifugal strength as 289 to 12868200, or as 1 to 44527, will be able to raise the waters in the places direct under and direct opposed to the sun to a height exceeding that in the places which are ninety degrees removed from the sun simply by ane Paris foot and 113 V inches ; for this measure out is to the measure of 85472 feet as 1 to 44527.

—Newton: Principia Corollary to Volume Two, Proposition XXXVI. Problem XVII

The effect of centrifugal strength in countering gravity, equally in this behavior of the tides, has led centrifugal force sometimes to be called "false gravity" or "fake gravity" or "quasi-gravity".^[eleven]

Eighteenth century [edit]

It wasn't until the latter half of the 18th century that the modern "fictitious force" understanding of the centrifugal strength as a pseudo-forcefulness antiquity of rotating reference frames took shape.^[12] In a 1746 memoir past Daniel Bernoulli, "the idea that the centrifugal strength is fictitious emerges unmistakably."^[13] Bernoulli, in seeking to describe the motion of an object relative to an capricious point, showed that the magnitude of the centrifugal force depended on which arbitrary signal was called to measure circular motion about. Later in the 18th century Joseph Louis Lagrange in his Mécanique Analytique explicitly stated that the centrifugal strength depends on the rotation of a organisation of perpendicular axes.^[thirteen] In 1835, Gaspard-Gustave Coriolis analyzed arbitrary motion in rotating systems, specifically in relation to waterwheels. He coined the phrase "compound centrifugal force" for a term which bore a like mathematical expression to that of centrifugal force, admitting that it was multiplied by a factor of two.^[xiv] The force in question was perpendicular to both the velocity of an object relative to a rotating frame of reference and the axis of rotation of the frame. Compound centrifugal strength somewhen came to be known as the Coriolis Force.^{[15] [sixteen]}

Absolute versus relative rotation [edit]

The thought of centrifugal force is closely related to the notion of accented rotation. In 1707 the Irish bishop George Berkeley took effect with the notion of absolute space, declaring that "move cannot be understood except in relation to our or some other body". In because a solitary globe, all forms of motility, uniform and accelerated, are unobservable in an otherwise empty universe.^[17] This notion was followed upward in modernistic times by Ernst Mach. For a single body in an empty universe, motion of any kind is inconceivable. Because rotation does not be, centrifugal force does non exist. Of class, improver of a speck of matter just to establish a reference frame cannot cause the sudden appearance of centrifugal strength, then it must be due to rotation relative to the unabridged mass of the universe.^[xviii] The modern view is that centrifugal force is indeed an indicator of rotation, but relative to those frames of reference that exhibit the simplest laws of physics.^[19] Thus, for example, if we wonder how speedily our galaxy is rotating, we tin brand a model of the galaxy in which its rotation plays a function. The rate of rotation in this model that makes the observations of (for example) the flatness of the galaxy concord best with physical laws equally nosotros know them is the best estimate of the rate of rotation^[twenty] (bold other observations are in agreement with this assessment, such every bit isotropy of the background radiation of the universe).^[21]

Role in developing the idea of inertial frames and relativity [edit]

In the rotating bucket experiment, Newton observed the shape of the surface of water in a bucket as the saucepan was spun on a rope. At first the water is flat, then, as it acquires the same rotation every bit the bucket, it becomes parabolic. Newton took this change every bit evidence that one could discover rotation relative to "absolute space" experimentally, in this instance by looking at the shape of the surface of the water.

Later scientists pointed out (as did Newton) that the laws of mechanics were the same for all observers that differed only by compatible translation; that is, all observers that differed in motion only past a constant velocity. Hence, "absolute space" was not preferred, but only ane of a set of frames related by Galilean transformations.^[22]

By the terminate of the nineteenth century, some physicists had concluded that the concept of accented space is not really needed...they used the law of inertia to define the unabridged class of inertial frames. Purged of the concept of absolute space, Newton's laws do single out the class of inertial frames of reference, but assert their complete equality for the description of all mechanical phenomena.

—Laurie M. Brown, Abraham Pais, A. B. Pippard: Twentieth Century Physics, pp. 256-257

Ultimately this notion of the transformation backdrop of physical laws between frames played a more than and more central role.^[23] Information technology was noted that accelerating frames exhibited "fictitious forces" similar the centrifugal forcefulness. These forces did not bear under transformation similar other forces, providing a means of distinguishing them. This peculiarity of these forces led to the names inertial forces, pseudo-forces or fictitious forces. In particular, fictitious forces did not announced at all in some frames: those frames differing from that of the fixed stars by only a constant velocity. In short, a frame tied to the "fixed stars" is merely a member of the form of "inertial frames", and accented space is an unnecessary and logically untenable concept. The preferred, or "inertial frames", were identifiable by the absence of fictitious forces.^{[24] [25] [26]}

The effect of his being in the noninertial frame is to require the observer to introduce a fictitious strength into his calculations….

—Sidney Borowitz and Lawrence A Bornstein in A Contemporary View of Elementary Physics, p. 138

The equations of motion in a not-inertial arrangement differ from the equations in an inertial arrangement past additional terms chosen inertial forces. This allows us to detect experimentally the non-inertial nature of a organisation.

—V. I. Arnol'd: Mathematical Methods of Classical Mechanics Second Edition, p. 129

The idea of an inertial frame was extended further in the special theory of relativity. This theory posited that all physical laws should appear of the aforementioned course in inertial frames, not merely the laws of mechanics. In detail, Maxwell's equations should apply in all frames. Because Maxwell's equations implied the same speed of light in the vacuum of free infinite for all inertial frames, inertial frames now were plant to be related not by Galilean transformations, but by Poincaré transformations, of which a subset is the Lorentz transformations. That posit led to many ramifications, including Lorentz contractions and relativity of simultaneity. Einstein succeeded, through many clever thought experiments, in showing that these apparently odd ramifications in fact had very natural caption upon looking at but how measurements and clocks really were used. That is, these ideas flowed from operational definitions of measurement coupled with the experimental confirmation of the constancy of the speed of lite.

After the general theory of relativity further generalized the idea of frame independence of the laws of physics, and abolished the special position of inertial frames, at the toll of introducing curved space-time. Following an analogy with centrifugal strength (sometimes chosen "artificial gravity" or "imitation gravity"), gravity itself became a fictitious forcefulness,^[27] equally enunciated in the equivalence principle.^[28]

The principle of equivalence: There is no experiment observers can perform to distinguish whether an acceleration arises because of a gravitational force or because their reference frame is accelerating

—Douglas C. Giancoli Physics for Scientists and Engineers with Modern Physics, p. 155

In short, centrifugal force played a key early role in establishing the set up of inertial frames of reference and the significance of fictitious forces, fifty-fifty aiding in the development of general relativity.

The mod conception [edit]

The mod interpretation is that centrifugal force in a rotating reference frame is a pseudo-force that appears in equations of motion in rotating frames of reference, to explain effects of inertia as seen in such frames.^[29]

Leibniz's centrifugal force may exist understood every bit an application of this formulation, as a result of his viewing the motility of a planet along the radius vector, that is, from the standpoint of a special reference frame rotating with the planet.^{[7] [eight] [30]} Leibniz introduced the notions of vis viva (kinetic energy)^[31] and activeness,^[32] which eventually establish full expression in the Lagrangian conception of mechanics. In deriving Leibniz's radial equation from the Lagrangian standpoint, a rotating reference frame is non used explicitly, but the result is equivalent to that found using Newtonian vector mechanics in a co-rotating reference frame.^{[33] [34] [35]}

References [edit]

1. ^ Domenico Bertoloni Meli (March 1990). "The Relativization of Centrifugal Forcefulness". Isis. The University of Chicago Press on behalf of The History of Scientific discipline Society. 81 (1): 23–43. doi:10.1086/355247. JSTOR 234081. S2CID 144526407.
2. ^ Soshichi Uchii (October 9, 2001). "Inertia". Retrieved 2008-05-25 .
3. ^ "Anni Mirabiles". Lapham's Quarterly . Retrieved 2020-08-27 . {{cite web}}: CS1 maint: url-status (link)
4. ^ The Mathematical Papers of Isaac Newton. Vol. Vi. Cambridge: University Press. 2008. ISBN978-0-521-04585-8.
5. ^ Donald Gillies (1995). Revolutions in Mathematics. Oxford: University Printing. p. 130. ISBN978-0-xix-851486-2.
6. ^ Herbert Goldstein (1980). Classical mechanics (2d ed.). Addison-Wesley. p. 74. ISBN978-0-201-02918-5.
7. ^ ^{a b c} Christopher M. Linton (2004). From Eudoxus to Einstein: a history of mathematical astronomy. Cambridge University Press. pp. 264–285. ISBN978-0-521-82750-8.
8. ^ ^{a b c} Frank Swetz (1997). Learn from the masters!. MAA. pp. 268–269. ISBN978-0-88385-703-8.
9. ^ ^{a b} "Newton, Sir Isaac". Retrieved 2008-05-25 .
10. ^ A. R. Hall, Philosophers at State of war, 2002, pp 150-151
11. ^ K. Novello, Matt Visser & Thousand. Eastward. Volovik (2002). Artificial blackness holes. World Scientific. p. 200. ISBN981-02-4807-5.
12. ^ Wilson (1994). "Newton's Orbit Problem: A Historian's Response". The Higher Mathematics Journal. Mathematical Association of America. 25 (3): 193–200. doi:10.2307/2687647. ISSN 0746-8342. JSTOR 2687647.
13. ^ ^{a b} Meli 1990, "The Relativization of Centrifugal Force".
14. ^ René Dugas and J. R. Maddox (1988). A History of Mechanics. Courier Dover Publications. p. 387. ISBN0-486-65632-ii.
15. ^ Persson, Anders (July 1998). "How Do Nosotros Understand the Coriolis Forcefulness?". Bulletin of the American Meteorological Lodge 79 (7): pp. 1373–1385. ISSN 0003-0007.
16. ^ Frederick Slate (1918). The Fundamental Equations of Dynamics and its Chief Coordinate Systems Vectorially Treated and Illustrated from Rigid Dynamics. Berkeley, CA: University of California Press. p. 137. compound centrifugal force coriolis.
17. ^ Edward Robert Harrison (2000). Cosmology (second ed.). Cambridge Academy Press. p. 237. ISBN0-521-66148-X.
18. ^ Ernst Mach (1915). The science of mechanics. The Open Court Publishing Co. p. 33. ISBN0-87548-202-3. Endeavor to set up Newton'south saucepan and rotate the heaven of fixed stars and so prove the absence of centrifugal forces
19. ^ J. F. Kiley, W. E. Carlo (1970). "The epistemology of Albert Einstein". Einstein and Aquinas. Springer. p. 27. ISBN90-247-0081-7.
20. ^ Henning Genz (2001). Pettiness. Da Capo Printing. p. 275. ISBN0-7382-0610-v.
21. ^ J. Garcio-Bellido (2005). "The Paradigm of Inflation". In J. K. T. Thompson (ed.). Advances in Astronomy. Majestic College Press. p. 32, §9. ISBN1-86094-577-5.
22. ^ Laurie M. Chocolate-brown, Abraham Pais & A. B. Pippard (1995). Twentieth Century Physics. CRC Press. pp. 256–257. ISBN0-7503-0310-seven.
23. ^ The idea of transformation properties of physical laws under various transformations is a cardinal topic in modernistic physics, related to such basic concepts as conservation laws similar conservation of free energy and momentum through Noether's theorem. See, for instance, Harvey R. Brown (2005). Physical Relativity. Oxford Academy Press. p. 180. ISBN0-nineteen-927583-ane. , and Gennady Gorelik (2002). Yuri Balashov; Vladimir Pavlovich Vizgin (eds.). Einstein Studies in Russia. Birkhäuser. p.The problem of conservation laws and the Poincare quasigroup in general relativity; pp. 17 ff. ISBN0-8176-4263-3. and Peter Mittelstaedt & Paul Weingartner (2005). Laws of Nature. Springer. p. 80. ISBNthree-540-24079-9.
24. ^ Milton A. Rothman (1989). Discovering the Natural Laws: The Experimental Ground of Physics . Courier Dover Publications. p. 23. ISBN0-486-26178-6. reference laws of physics.
25. ^ Sidney Borowitz & Lawrence A. Bornstein (1968). A Contemporary View of Unproblematic Physics. McGraw-Hill. p. 138. ASIN B000GQB02A.
26. ^ V. I. Arnol'd (1989). Mathematical Methods of Classical Mechanics. Springer. p. 129. ISBN978-0-387-96890-2.
27. ^ Hans Christian Von Baeyer (2001). The Fermi Solution: Essays on science (Reprint of 1993 ed.). Courier Dover Publications. p. 78. ISBN0-486-41707-7.
28. ^ Douglas C. Giancoli (2007). Physics for Scientists and Engineers with Modern Physics. Pearson Prentice Hall. p. 155. ISBN978-0-xiii-149508-ane.
29. ^ Charles Proteus Steinmetz (2005). Four Lectures on Relativity and Infinite. Kessinger Publishing. p. 49. ISBN1-4179-2530-2.
30. ^ E. J. Aiton (1 March 1962). "The celestial mechanics of Leibniz in the calorie-free of Newtonian criticism". Annals of Science. Taylor & Francis. 18 (1): 31–41. doi:x.1080/00033796200202682.
31. ^ Bertrand Russell (1992). A Critical Exposition of the Philosophy of Leibniz (Reprint of 1937 2nd ed.). Routledge. p. 96. ISBN0-415-08296-10.
32. ^ Wolfgang Lefèvre (2001). Between Leibniz, Newton, and Kant. Springer. p. 39. ISBN0-7923-7198-four.
33. ^ Herbert Goldstein (2002). Classical Mechanics. San Francisco : Addison Wesley. pp. 74–77, 176. ISBN0-201-31611-0.
34. ^ John Taylor (2005). Classical Mechanics. University Science Books. pp. 358–359. ISBN1-891389-22-X.
35. ^ Whiting, J.Southward.S. (November 1983). "Motion in a key-strength field" (PDF). Physics Educational activity. eighteen (6): 256–257. Bibcode:1983PhyEd..eighteen..256W. doi:10.1088/0031-9120/eighteen/six/102. ISSN 0031-9120. Retrieved May 7, 2009.

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Source: https://en.wikipedia.org/wiki/History_of_centrifugal_and_centripetal_forces

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