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| {{About|the physics experiment and implement|the novel by Italian philosopher Umberto Eco|Foucault's Pendulum}}
| | The most important thing is that you should be aware of all the causes so that you can prevent this ailment from occurring. There are many home based remedies available in yeast infection cure. When the amount of Candida increase, it leads to imbalance and causes yeast infection, leading to uncomfortable and embarrassing feeling for its sufferers. On the flip side of the coin, cotton is known to offer better aeration than synthetic materials and can really help in regulating heat and dampness. this itching is not always present, but can get really bad, so bad you can hardly walk. <br><br>Do not let this build up of sweat around the body irritate the yeast condition. Unlike over the counter treatments and doctors prescriptions, natural cures work with your body. Many women have had a yeast infection in their lifetime. We all possess a variety of kinds of bacteria in our bodies and nearly all of them are required for all round good health. Using tea tree oil will kill the excess Candida, thus eliminating yeast infection. <br><br>There are 3 main symptoms of a yeast infection, the first is itchiness in the vulva and surrounding areas, it can become so unbearable at times. They are much larger - about 10 times more than the bacterial cells, moreover yeast cells may be found to be oval in shape unlike the bacterial cells which are mostly elongated. When the skin is already infected by bacteria and fungus, it can easily spread all over and most of time with swelling. Colloidal Silver; use neat directly to the web site - a spray bottle functions definitely effectively right here. There are in fact, alternative, cheap, safe, natural and holistic health practices and methods necessary to permanently eliminate the symptoms of this disease and cure the root internal cause of yeast infection regardless of its type, location, or level of severity. <br><br>Vaginal yeast infections impact millions of women and with the right treatments can be get rid of easily. Sometimes, even low vitamin A, increase in the carotene level, or abnormally high cholesterol could indicate hypothyroidism. Wearing the wrong type of clothing can actually help your body foster a Yeast Infections. Other versions of the T-Gel shampoo have different active ingredients. Moyer: Vaginal yeast infections are usually not sexually transmitted. <br><br>This will weaken the immune system and will result in Candida overgrowth. Garlic is another option you have at your disposal. This typically happens only during times of menstruation. If you're intrigued but still not keen on applying yeast infection cream on your scalp, you may be happy to know that some hair loss sufferers are using dandruff shampoos with similar results. Of course, you can use probiotics capsules and suppositories from the pharmacy as an alternative.<br><br>In the event you cherished this information in addition to you desire to get guidance relating to get rid of yeast infection, [http://www.naturalcureyeastinfection.info/ click for more info], generously pay a visit to our page. |
| [[File:California Academy of Sciences Foucault Pendulum Clock.jpg|thumb|300px|A Foucault pendulum installed at the [[California Academy of Sciences]]. The Earth's rotation causes the trajectory of the pendulum to change over time, knocking down pins at different positions as time elapses and the Earth rotates]]
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| [[File:Foucault pendulum animated.gif|right|thumb|In this animation the rate of precession is greatly exaggerated. The Foucault pendulum in 1851 was the first demonstration of the Earth's rotation that did not involve celestial observations, and it created a "pendulum mania".]]
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| The '''Foucault pendulum''' ({{IPAc-en|lang|pron|f|uː|ˈ|k|oʊ}} {{respell|foo|KOH|'}}; {{IPA-fr|fuˈko}}), or '''Foucault's pendulum''', named after the French physicist [[Léon Foucault]], is a simple device conceived as an experiment to demonstrate the [[Earth's rotation|rotation of the Earth]]. While it had long been known that the [[Earth]] rotated, the introduction of the Foucault pendulum in 1851 was the first simple proof of the rotation in an easy-to-see experiment. Today, Foucault pendulums are popular displays in science museums and universities.
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| == Original Foucault pendulum ==
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| [[File:Pendule de Foucault.jpg|thumb|300px|Foucault's Pendulum in the [[Panthéon, Paris]]]]
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| [[File:Péndulo de Foucault-20110815-125224-2191-1000d-a2b2.jpg|thumb|right|160px|The Foucault pendulum at Panthéon, Paris.]]
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| The first public exhibition of a Foucault pendulum took place in February 1851 in the Meridian of the [[Paris Observatory]]. A few weeks later Foucault made his most famous pendulum when he suspended a 28 kg brass-coated lead [[bob (physics)|bob]] with a 67 meter long wire from the dome of the [[Panthéon, Paris]]. The plane of the pendulum's swing rotated clockwise 11° per hour, making a full circle in 32.7 hours. The original bob used in 1851 at the Panthéon was moved in 1855 to the [[Conservatoire des Arts et Métiers]] in Paris. A second temporary installation was made for the 50th anniversary in 1902.<ref>{{cite web |url=http://www.parisenimages.fr/en/popup-photo.html?photo=9232-13 |title=The Pendulum of Foucault of the Panthéon. Ceremony of inauguration by M. Chaumié, minister of the state education, burnt the wire of balancing, to start the Pendulum. 1902 |publisher=Paris en images}}</ref>
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| During museum reconstruction in the 1990s the original pendulum was temporarily displayed at the Panthéon (1995), but was later returned to the [[Musée des Arts et Métiers]] before it reopened in 2000.<ref>{{cite web|last=Kissell|first=Joe|title=Foucault’s Pendulum: Low-tech proof of Earth’s rotation|url=http://itotd.com/articles/362/foucaults-pendulum/|publisher=Interesting thing of the day|accessdate=March 21, 2012|date=November 8, 2004}}</ref> On April 6, 2010 the cable suspending the bob in the Musée des Arts et Métiers snapped, causing irreparable damage to the pendulum and to the marble flooring of the museum.<ref>{{cite news |url=http://www.lexpress.fr/actualite/sciences/le-pendule-de-foucault-perd-la-boule_888228.html |title=Le pendule de Foucault perd la boule |first=Boris |last=Thiolay |publisher=L'Express |date=April 28, 2010}} {{fr icon}}</ref><ref>{{cite news |title=Foucault's pendulum is sent crashing to Earth |url=http://www.timeshighereducation.co.uk/story.asp?storycode=411529|accessdate=March 21, 2012|newspaper=Times Higher Education|date=13 May 2010}}</ref> An exact copy of the original pendulum has been swinging permanently since 1995 under the dome of the Panthéon, Paris.
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| [[File:Foucault pendulum at north pole accurate.PNG|thumb|left|160px|A Foucault pendulum at the north pole. The pendulum swings in the same plane as the Earth rotates beneath it.]]
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| == Explanation of mechanics ==
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| The experimental apparatus consists of a tall [[pendulum]] free to swing in any vertical plane. The actual plane of swing appears to rotate relative to the Earth. The wire needs to be as long as possible—lengths of 12–30 m (40–100 ft) are common.<ref>
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| {{cite web|title=Foucault Pendulum|publisher=Smithsonian Encyclopedia|url=http://www.si.edu/Encyclopedia_SI/nmah/pendulum.htm|accessdate=Sep 2, 2013}}
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| </ref> | |
| [[File:Foucault-rotz.gif|250px|thumb|right|Animation of a Foucault pendulum at the Pantheon in Paris (48°52' North), with the Earth's rotation rate greatly exaggerated. The green trace shows the path of the pendulum bob over the ground (a rotating reference frame), while the blue trace shows the path in a frame of reference rotating with the plane of the pendulum.]]
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| At either the [[North Pole]] or [[South Pole]], the plane of oscillation of a pendulum remains fixed relative to the [[Mach's principle|distant masses of the universe]] while Earth rotates underneath it, taking one [[sidereal day]] to complete a rotation. So, relative to Earth, the plane of oscillation of a pendulum at the North Pole undergoes a full clockwise rotation during one day; a pendulum at the South Pole rotates counterclockwise.
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| When a Foucault pendulum is suspended at the [[equator]], the plane of oscillation remains fixed relative to Earth. At other latitudes, the plane of oscillation [[Precession|precesses]] relative to Earth, but slower than at the pole; the angular speed, ''ω'' (measured in clockwise [[degree (angle)|degrees]] per sidereal day), is proportional to the [[sine]] of the [[latitude]], ''φ'':
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| :<math>\omega=360\sin\varphi\ ^\circ/\mathrm{day}</math>
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| where latitudes north and south of the equator are defined as positive and negative, respectively. For example, a Foucault pendulum at 30° south latitude, viewed from above by an earthbound observer, rotates counterclockwise 360° in two days.
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| In order to demonstrate the rotation of the Earth without the complication of the dependence on latitude, Foucault used a [[gyroscope]] in an 1852 experiment. The gyroscope's spinning rotor tracks the stars directly. Its axis of rotation is observed to return to its original orientation with respect to the earth after one day whatever the latitude, not being subject to the unbalanced [[Coriolis effect|Coriolis]] forces acting on the pendulum as a result of its geometric asymmetry.
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| [[File:Foucault Pendulum - Ranchi Science Centre - Jharkhand 2010-11-29 8871.JPG|thumb|left|200px|Foucault's Pendulum at the [[Ranchi Science Centre]].]]
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| A Foucault pendulum requires care to set up because imprecise construction can cause additional veering which masks the terrestrial effect. The initial launch of the pendulum is critical; the traditional way to do this is to use a flame to burn through a thread which temporarily holds the bob in its starting position, thus avoiding unwanted sideways motion. [[Air resistance]] damps the oscillation, so some Foucault pendulums in museums incorporate an electromagnetic or other drive to keep the bob swinging; others are restarted regularly, sometimes with a launching ceremony as an added attraction.
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| A ''pendulum day'' is the time needed for the plane of a freely suspended Foucault pendulum to complete an apparent rotation about the local vertical. This is one sidereal day divided by the sine of the latitude.<ref>{{cite web |url=http://amsglossary.allenpress.com/glossary/search?id=pendulum-day1 |title=Pendulum day |work= Glossary of Meteorology |publisher=American Meteorological Society}}</ref>
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| == Precession as a form of parallel transport ==
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| [[File:Small rotation angle.gif|frame|right|Change of direction of the plane of swing of the pendulum in [[angle]] per sidereal day as a function of latitude. The pendulum rotates in the anticlockwise (positive) direction on the southern hemisphere and in the clockwise (negative) direction on the northern hemisphere. The only points where the pendulum returns to its original orientation after one day are the poles and the equator.]]
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| [[File:Parallel transport.png|280px|thumb|right|Parallel transport of a vector around a closed loop on the sphere. The angle by which it twists, <math>\alpha</math>, is proportional to the area inside the loop.]]
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| From the perspective of an inertial frame moving in tandem with Earth, but not sharing its rotation, the suspension point of the pendulum traces out a circular path during one sidereal day. At the latitude of Paris a full precession cycle takes 32 hours, so after one sidereal day, when the Earth is back in the same orientation as one sidereal day before, the oscillation plane has turned 90 degrees. If the plane of swing was north-south at the outset, it is east-west one sidereal day later. This implies that there has been exchange of momentum; the Earth and the pendulum bob have exchanged momentum. The Earth is so much more massive than the pendulum bob that the Earth's change of momentum is unnoticeable. Nonetheless, since the pendulum bob's plane of swing has shifted the conservation laws imply that there must have been exchange.
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| Rather than tracking the change of momentum, the precession of the oscillation plane can efficiently be described as a case of [[parallel transport]]. For that it is assumed that the precession rate is proportional to the [[Orthogonal projection|projection]] of the [[angular velocity]] of Earth onto the [[Normal (geometry)|normal]] direction to Earth, which implies that the plane of oscillation will undergo parallel transport. The difference between initial and final orientations is {{nowrap|''α'' {{=}} −2 sin(''φ'')}}, in which case the [[Gauss-Bonnet theorem]] applies. ''α'' is also called the [[holonomy]] or [[geometric phase]] of the pendulum. Thus, when analyzing earthbound motions, the Earth frame is not an [[inertial frame]], but rather rotates about the local vertical at an effective rate of {{nowrap|2π sin(''φ'')}} radians per day.
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| A simple method employing parallel transport within cones tangent to the Earth's surface can be used to describe
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| the rotation angle of the swing plane of Foucault's pendulum.<ref>W. B. Somerville, [http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1972QJRAS..13...40S&data_type=PDF_HIGH&whole_paper=YES&type=PRINTER&filetype=.pdf "The Description of Foucault's Pendulum"], ''Q. J. R. Astron''. Soc. 13, 40 (1972).
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| </ref><ref>J. B. Hart, R. E. Miller and [[Robert Mills (physicist)|R. L. Mills]],
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| [http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=AJPIAS000055000001000067000001&idtype=cvips&gifs=yes&ref=no "A simple geometric model for visualizing the motion of a Foucault pendulum"], ''Am. J. Phys''. 55, 67–70 (1987).
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| </ref>
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| From the perspective of an Earth-bound coordinate system with its ''x''-axis pointing east and its ''y''-axis pointing north, the precession of the pendulum is described by the [[Coriolis force]]. Consider a planar pendulum with natural frequency ''ω'' in the [[small angle approximation]]. There are two forces acting on the pendulum bob: the restoring force provided by gravity and the wire, and the Coriolis force. The Coriolis force at latitude ''φ'' is horizontal in the small angle approximation and is given by
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| :<math>
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| \begin{align}
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| F_{c,x} &= 2 m \Omega \dfrac{dy}{dt} \sin(\varphi)\\
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| F_{c,y} &= - 2 m \Omega \dfrac{dx}{dt} \sin(\varphi)
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| \end{align}
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| </math>
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| where Ω is the rotational frequency of Earth, ''F<sub>c'',''x</sub>'' is the component of the Coriolis force in the ''x''-direction and ''F<sub>c'',''y</sub>'' is the component of the Coriolis force in the ''y''-direction.
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| The restoring force, in the small angle approximation, is given by
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| :<math>
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| \begin{align}
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| F_{g,x} &= - m \omega^2 x \\
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| F_{g,y} &= - m \omega^2 y.
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| \end{align}
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| </math>
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| Using [[Newton's laws of motion]] this leads to the system of equations
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| :<math>
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| \begin{align}
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| \dfrac{d^2x}{dt^2} &= -\omega^2 x + 2 \Omega \dfrac{dy}{dt} \sin(\varphi)\\
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| \dfrac{d^2y}{dt^2} &= -\omega^2 y - 2 \Omega \dfrac{dx}{dt} \sin(\varphi) \,.
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| \end{align}
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| </math>
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| Switching to complex coordinates {{nowrap|''z'' {{=}} ''x'' + ''iy''}}, the equations read
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| :<math>\frac{d^2z}{dt^2} + 2i\Omega \frac{dz}{dt} \sin(\varphi)+\omega^2 z=0 \,.</math>
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| To first order in Ω/''ω'' this equation has the solution
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| :<math>z=e^{-i\Omega \sin(\varphi) t}\left(c_1 e^{i\omega t}+c_2 e^{-i\omega t}\right) \,.</math>
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| If we measure time in days, then {{nowrap|Ω {{=}} 2π}} and we see that the pendulum rotates by an angle of −2π sin(''φ'') during one day.
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| <!--Foucault's original paper (Comptes Rendus Vol.32, 1851, p.135) is wholly descriptive. He remarks in effect that the rate of precession of the plane of rotation can be obtained analytically or geometrically. From a geometric perspective much of the explanation given above comes down to the statement that the rate of change of azimuth of a star on the horizon depends only on the observer's latitude and is the same as the rate of precession of the pendulum (Journal of the Royal Astronomical Society of Canada, Vol.63,1970, pp. 227–228). Binet (Comptes Rendus Vol.32, 1851, p.197) gives a simple analytical derivation of the rate. [[Arthur Cayley]] (Collected Works Vol.4,1891, pp. 534–537) says that[[Poisson]] examined the problem in 1838 and concluded that there would be no effect due to the rotation of the Earth. [[Kamerlingh Onnes]] based his doctoral dissertation on the accurate determination of the Earth's rotation by means of the pendulum
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| (Schulz-DuBois, American Journal of Physics, Vo.28, 1970, p.173). -->
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| == Related physical systems ==
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| [[File:Wheatstone Foucault device 256x256.png|thumb|right|200px|The device described by Wheatstone.]]
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| There are many physical systems that precess in a similar manner to a Foucault pendulum. As early as 1836, [[Edward Sang]] contrived and explained the precession of a spinning [http://books.google.fr/books?id=rtpQAAAAYAAJ&pg=PA105 top]. In 1851, [[Charles Wheatstone]]
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| <ref>[[Charles Wheatstone]] Wikisource: "[[s:Note relating to M. Foucault's new mechanical proof of the Rotation of the Earth|Note relating to M. Foucault's new mechanical proof of the Rotation of the Earth]]", pp. 65–68.</ref> described an apparatus that consists of a vibrating spring that is mounted on top of a disk so that it makes a fixed angle <math>\phi</math> with the disk. The spring is struck so that it oscillates in a plane. When the disk is turned, the plane of oscillation changes just like the one of a Foucault pendulum at latitude <math>\phi</math>. | |
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| Similarly, consider a non-spinning perfectly balanced bicycle wheel mounted on a disk so that its axis of rotation makes an angle <math>\phi</math> with the disk. When the disk undergoes a full clockwise revolution, the bicycle wheel will not return to its original position, but will have undergone a net rotation of <math>2\pi\, \sin(\phi)</math>.
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| Another system behaving like a Foucault pendulum is a [[South Pointing Chariot]] that is run along a circle of fixed latitude on a globe. If the globe is not rotating in an inertial frame, the pointer on top of the chariot will indicate the direction of swing of a Foucault pendulum that is traversing this latitude.
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| Spin of a relativistic particle moving in a circular orbit precesses similar to the swing plane of Foucault pendulum. The relativistic velocity space in [[Minkowski spacetime]] can be treated as a sphere ''S''<sup>3</sup> in 4-dimensional [[Euclidean space]] with imaginary radius and imaginary timelike coordinate. Parallel transport of polarization vectors along such sphere gives rise to [[Thomas precession]], which is analogous to the rotation of the swing plane of Foucault pendulum due to parallel transport along a sphere ''S''<sup>2</sup> in 3-dimensional Euclidean space.<ref>M. I. Krivoruchenko, [http://arxiv.org/abs/0805.1136 "Rotation of the swing plane of Foucault's pendulum and Thomas spin precession: Two faces of one coin"], ''Phys. Usp.'' 52, 821–829 (2009).</ref>
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| In physics, the evolution of such systems is determined by [[geometric phase]]s.<ref>"Geometric Phases in Physics", eds. [[Frank Wilczek]] and Alfred Shapere (World Scientific, Singapore, 1989).</ref><ref>L. Mangiarotti, G. [[Sardanashvily]], [http://books.google.com/books?id=-N6F44hlnhgC&pg=PA281&dq=%22Berry+connection%22&lr=&as_brr=0''Gauge Mechanics''] (World Scientific, Singapore, 1998)</ref> Mathematically they are understood through parallel transport. | |
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| [[File:Foucault pendulum plane of swing semi3D.gif|frame|The animation describes the motion of a Foucault Pendulum at a latitude of 30°N. The plane of oscillation rotates by an angle of −180° during one day, so after two days the plane returns to its original orientation.]]
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| == Foucault pendulums around the world ==
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| {{Further|List of Foucault pendulums}}
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| There are numerous Foucault pendulums around the world, mainly at universities, science museums and planetariums. The [[United Nations]] headquarters in [[New York City]] has one, while the largest Foucault pendulum in the world, ''Principia'', is housed at the [[Oregon Convention Center]].<ref>http://ltwautomation.net/casestudies.html#Pendulum</ref>
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| ==== South Pole ====
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| The experiment has also been carried out at the [[South Pole]], where it was assumed that the rotation of the earth would have little effect. The South Pole Pendulum Project (as discussed in ''[[The New York Times]]''<ref>{{cite news |title=Here They Are, Science's 10 Most Beautiful Experiments |first=George |last=Johnson |url=http://www.nytimes.com/2002/09/24/science/here-they-are-science-s-10-most-beautiful-experiments.html?pagewanted=all&src=pm |newspaper=The New York Times |date=September 24, 2002 |accessdate=September 20, 2012}}</ref> and excerpted from ''Seven Tales of the Pendulum''<ref>{{cite book |last=Baker |first=G. P. |year=2011 |title=Seven Tales of the Pendulum |pages=388 |publisher=[[Oxford University Press]] |isbn=978-0-19-958951-7}}</ref>) was constructed and tested by adventurous experimenters John Bird, Jennifer McCallum, Michael Town, and Alan Baker at the [[Amundsen-Scott South Pole Station]]. Their measurement is probably the closest ever made to one of the earth’s poles. The pendulum was erected in a six-story staircase of a new station that was under construction near the pole. Conditions were challenging; the altitude was about 3,300 metres (atmospheric pressure only about 65 percent that at sea level) and the temperature in the unheated staircase was about {{convert|-68|°C|°F}}. The pendulum had a length of 33 meters and a 25 kilogram bob. The new station offered an ideal venue for the Foucault pendulum; its height ensured an accurate result, no moving air could disturb it, and low air pressure reduced air resistance. The researchers confirmed about 24 hours as the rotation period of the plane of oscillation.
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| == References ==
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| {{reflist}}
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| == Further reading ==
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| * Persson, A. [http://www.meteohistory.org/2005historyofmeteorology2/01persson.pdf "The Coriolis Effect: Four centuries of conflict between common sense and mathematics, Part I: A history to 1885"] ''History of Meteorology'' 2 (2005)
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| * ''Classical dynamics of particles and systems'', 4ed, Marion Thornton ISBN 0-03-097302-3, pp. 398–401.
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| * V. I. Arnold, ''Mathematical Methods of Classical Mechanics'', Springer-Verlag (1989), ISBN 0-387-96890-3, p. 123
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| == External links ==
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| {{Commons category}}
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| * Julian Rubin, [http://www.juliantrubin.com/bigten/foucaultpendulum.html "The Invention of the Foucault Pendulum"], Following the Path of Discovery, 2007, retrieved 2007-10-31. Directions for repeating Foucault's experiment, on amateur science site.
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| * Wolfe, Joe, "[http://www.phys.unsw.edu.au/~jw/pendulumdetails.html A derivation of the precession of the Foucault pendulum]".
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| * "[http://www.sciencebits.com/foucault The Foucault Pendulum]", derivation of the precession in polar coordinates.
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| * "[http://www.phys.unsw.edu.au/PHYSICS_!/FOUCAULT_PENDULUM/foucault_pendulum.html The Foucault Pendulum]" By Joe Wolfe, with film clip and animations.
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| * "[http://demonstrations.wolfram.com/FoucaultsPendulum/ Foucault's Pendulum]" by Jens-Peer Kuska with Jeff Bryant, [[Wolfram Demonstrations Project]]: a computer model of the pendulum allowing manipulation of pendulum frequency, Earth rotation frequency, latitude, and time.
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| * "[http://pendelcam.kip.uni-heidelberg.de/ Webcam Kirchhoff-Institut für Physik, Universität Heidelberg]".
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| * [http://www.calacademy.org/products/pendulum/index.html California academy of sciences, CA] Foucault pendulum explanation, in friendly format
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| * [http://electron.physics.buffalo.edu/ubexpo/Foucault%20Pendulum.html Foucault pendulum model] Exposition including a tabletop device that shows the Foucault effect in seconds.
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| * Foucault, M. L., [http://www.fi.edu/time/journey/Pendulum/foucault_paper_page_one.html ''Physical demonstration of the rotation of the Earth by means of the pendulum''], Franklin Institute, 2000, retrieved 2007-10-31. Translation of his paper on Foucault pendulum.
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| * Tobin, William [http://www2.phys.canterbury.ac.nz/~wjt23/foucault.html "The Life and Science of Léon Foucault"].
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| * {{cite web|last=Bowley|first=Roger|title=Foucault's Pendulum|url=http://www.sixtysymbols.com/videos/foucault.htm|work=Sixty Symbols|publisher=[[Brady Haran]] for [[University of Nottingham]]|year=2010}}
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| * [http://www.fizkapu.hu/fizfilm/fizfilm1.html Foucault-inga Párizsban] ''Foucault's Pendulum in Paris'' – video of the operating Foucault's Pendulum in the Panthéon {{hu}}.
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| * [http://www.labtrek.it/libroPF_rid.pdf Pendolo nel Salone] The Foucault Pendulum inside Palazzo della Ragione in Padova, Italy
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| [[Category:Pendulums]]
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