Talk:Foucault pendulum

Pendulum on the Equator
Interestingly, although the article states that "When a Foucault pendulum is suspended on the equator, the plane of oscillation remains fixed relative to Earth." this has never been tested - perhaps not unsurprisingly..... Thomas Goodey

There should be more info please???????
 * If you understand the situation at a pole: the Earth is rotating but not the plane of oscillations which is fixed to stars and not Earth, you could understand the situation at the equator. Earth is not rotating around a vertical axis at the equator. If you look at the stars at the equator, they do not draw circles but lines, but at the pole they are circling. More precisely, if at the pole, you were following a specific star, the trajectory of this specific star will be a single point but the trajectories of some stars around it are circles which will not end in one day but in a longer time which depends on how high was your chosen fixed star in the sky. If the angle is 90 degrees, you will find the Polar star and the stars around will circle in 24 hours, but if your angle is 48 degrees like in Paris and find a star at that angle and follow it, the stars around it will circle in 24/sin(48°). And if you find a star at the horizon, stars around it will not circle at all. This is what happens will the Foucault pendulum. Hope that helps you.--Nbrouard (talk) 15:19, 14 February 2015 (UTC)

eclipses
A recent BBC news article about eclipses had the following quote: "For example, long period Foucault pendulums - designed to demonstrate the rotation of the Earth - have been known to swing wildly during eclipses."

- http://news.bbc.co.uk/2/hi/science/nature/7347180.stm

That looks like something which should be verified and added to the article? --.../Nemo (talk) 00:05, 22 May 2008 (UTC)


 * I have come across references to reports of anomalies in Foucault pendulum motion during eclipses. It is my understanding that the magnitude of the anomalies was so small that it is very difficult to distinguish them from the various perturbing influences that make a Foucault pendulum deviate from the motion predicted by the mathematical models. So for one thing it is not certain that the described anomalies cannot be accounted for in terms of known perturbative factors. Since solar eclipses are very rare and are very short in duration, it's very difficult to set up an experiment. In my opinion the 'anomalies during eclipses' story doesn't merit inclusion in the wikipedia article. --Cleonis | Talk 21:54, 22 May 2008 (UTC)


 * It's called the Allais effect. It's a bunch of crap, which is why, when I suggested it be mentioned here, it was decided to leave it out.Rracecarr (talk) 03:08, 10 July 2008 (UTC)


 * Isn't the cause just the draught of all the people rushing outside to see the eclipse?  D b f i r s   22:08, 9 February 2010 (UTC)

Pantheon Pendulum
I'm wondering if anybody knows anything specifically about the pendulum in the Paris pantheon. How does it keep moving? 69.220.2.188 (talk) 01:36, 10 July 2008 (UTC)
 * Please have a look at the Fernand Charron's annular (1931) in the French wikipedia. It has been used at the Palais de la Découverte's pendulum in Paris for a while. Now, and for most recent pendulums, there is probably something different.--Nbrouard (talk) 14:25, 20 November 2008 (UTC)

Comprehensible explanation needed
This article needs work. I'm a lay person who usually understands scientific topics pretty well. There is nothing in this article that helps me understand the phenomenon. The lay-level section doesn't attempt to explain it, and the technical section is extremely opaque. The special cases of the poles and equator make sense to me, and I can see that there must be a transition from one to the other, but in both those cases, the pendulum is in the same position at the completion of one rotation. Understanding that the pendulum is going to process, it is still extremely counter-intuitive that after the earth has returned to the start position, the pendulum swings at some different angle. Someone who gets it needs to write an explanation that at least a generally scientifically literate college graduate, if not a high school student, can understand. Craig Butz (talk) 00:25, 15 September 2008 (UTC)


 * Indeed, it's not easy to understand the precession of the pendulum intuitively. I recently made a toy paper model, which may help your understanding: Use a Piece of Paper, to Understand the Foucault Pendulum --Kuh96 (talk) 06:46, 3 June 2015 (UTC)
 * I agree, it is hard to understand. 2001:861:5B80:8950:C09D:3997:7FC3:3886 (talk) 05:05, 9 August 2022 (UTC)

As a layman, I would find it really helpful if the article could answer the following question, which has always bugged me ever since I saw a Foucalt Pendulum: "OK, so the plane of the swing of the pendulum is not stationary with regard to the Earth. Is it stationary in relation to anything else - the centre of gravity of the galaxy, or of the universe?  If not, then what?" I think an article which answered that question would have to be a lot clearer, better structured and illuminating. I only wish I could write it! —Preceding unsigned comment added by AnthonyConway (talk • contribs) 15:22, 15 September 2008 (UTC)


 * The language of physics and reference frames goes like this: The plane-of-swing of a pendulum is not fixed relative to the surface of the Earth, but it is fixed relative to the Earth’s rotational axis. The Earth’s axis is fixed (the Earth is a giant gyroscope) and every point on the Earth’s surface, except the two poles, rotates around this axis once every 24 hours. The hinge points of all pendulums are also attached to the Earth’s surface, but the planes-of-swing of all pendulums are not influenced by the gravitational force on the pendulum bobs. Consequently the planes-of-swing remain fixed in their orientation relative to the star field and the Earth’s axis - we describe this orientation as “fixed in the reference frame of the Earth’s rotational axis.” Dolphin ( t ) 06:45, 9 August 2022 (UTC)
 * But this isn't true. As one of the animations (and the math) shows, a Foucault pendulum at 30 degrees from the equator that starts off swinging north-south will be swinging east-west 12 hours later. Craig Butz (talk) 05:29, 30 October 2023 (UTC)


 * Clearly it's not stationary in relation to anything. If you take 3 foucault pendula, one at the north pole, one at the equator, and one at 48.59 degrees north, and start them all swinging in the same north-south plane, at the end of a sidereal day, the one at the north pole will be swinging in the same plane, having stayed that way (relative to the stars) all day, but having appeared to have rotated 360 degrees relative to the the ground; the one on the equator will have appeared to have stayed stationary from earth, but its plane of motion will have rotated 360 degrees with along with the earth; and the one at 48.59 degrees will have rotated 270 degrees and be swinging east-west.  As I try to wrap my mind around this, I'd say that the pendulum is trying to stay in the same plane, but is constrained by gravity which changes direction with the rotation of the earth. At the pole it is able to maintain its swinging plane because gravity is pulling consistently down the axis of rotation, causing no change relative to the stars.  At the equator, it is totally unable to maintain the plane because the center of gravity that it must stay oriented to is perpendicular to the axis and rotates an entire 360 degrees around the pendulum.  As you move north, the deviation caused by gravity is reduced as the center of gravity gets closer to the same direction as the axis of rotation.  It's beginning to make sense to me, I think. Craig Butz (talk) 22:12, 20 September 2008 (UTC)

It is difficult to be concise and precise and I have not succeeded in the past. Here is another attempt at a lay-level discussion for comment. It is helpful to create a diagram of a simplified pendulum apparatus as an aid in visualizing the interaction. A Foucault Pendulum experiment demonstrates the interaction of the plane of swing of the pendulum with a gravitational line of force with the pendulum suspended from a rotating frame of reference (Earth). Because a rotational frame of reference is necessary for the observed effect the Foucault pendulum experiment demonstrates that the Earth turns. The Sine Law for the Foucault pendulum (that the period of the plane of swing is inversely proportional to the sine of the latitude of the location) describes the observed increase in rotational period of the pendulum swing compared to the rotation of the Earth that occurs with a decrease in latitude of the suspension point of the plumb line. The period of the pendulum swing changes from one day at the poles where the gravitational plumb line of the pendulum is perpendicular to the the rotational plane of the Earth but increases to an infinite (undefined) period at the equator where th plumb line is parallel to the rotational plane of the Earth.

The plane of swing of the pendulum has precession in the opposite direction of the rotating frame of reference when the gravitational plumb line is no longer aligned with the axis of rotation. The period of the precession increases as the angle increases between the gravitational plumb line and the axis of rotation line (from a period of precession of zero at the poles where the angle is zero or the two reference lines are parallel to a period of precession of 1 day when the angle is 90 or the two reference lines are perpendicular). The increase in the period of precession results in the increase in the period of the pendulum swing in accord with the Pendulum Sine Law identified by Foucault. The increase in precession from zero at the poles to 1 day at the equator is identified as part of the Coriolis Effect.

Alternatively, from a point-of-view independent from the rotating reference frame of the Earth that is included in the plane of swing of the pendulum, the Earth is observed to turn under the plane of swing with a period of one day for the turning of the Earth for an apparatus at the poles in reference to the plane of swing. As the angle between the gravitational plumb line and the axis of rotation is increased then the angular velocity of the Earth in reference to the plane of swing is observed to decrease with the sine of the angle of alignment (or the period for a full rotation of the plane of swing to be observed increases in accordance with the Pendulum Sine Law where the period increases inversely with the sine of 90 minus the angle of alignment, or the sine of the latitude of the location.David Harty (talk) 07:35, 16 September 2008 (UTC)

David, thanks for trying, but it still begs the question, what exactly is the "point-of-view independent from the rotating reference frame of the Earth" relative to which the plane of the pendulum's swing does not rotate. It's obviously not any old random frame of reference, it's the one relative to which the plane of the pendulum's swing does not rotate. Can it be defined in any other way? 62.189.189.132 (talk) 10:30, 16 September 2008 (UTC)


 * The independent frame of reference is one that isn't rotating in relation to the fixed stars. But the pendulum's swinging does change relative even to that (except at the pole.) As I understand it, rotation isn't relative.  Even if you are in an empty part of the universe, unable to see a single star, you can tell whether you are absolutely still or rotating because of centrifugal force.Craig Butz (talk) 13:57, 22 September 2008 (UTC)


 * The paragraphs above discuss the difference in perspective depending on the location or point-of-viewing. The different viewing points are 1) an Earth-bound frame of reference next to the pendulum, 2) a non-rotational frame of reference separated from the Earth, and 3) a frame of reference always in the plane of swing of the pendulum.


 * Another lay-level discussion might consider the Coriolis Effect. The increase in precession of the plane of swing from zero at the poles to 1 day at the equator is part of the Coriolis Effect.  The effect occurs because the mass of the pendulum bob has inertia in the initiated plane of direction that opposes the change of direction due to the rotation of the Earth.  In a rotating reference frame an object has inertia (interpreted as inertial circles) to maintain motion in a certain initiated direction even though a rotational force is being applied.  The inertia results in the observed motion in opposition to the rotational reference frame.


 * Suppose it were possible to construct a Foucault Pendulum experiment at a latitude such as 45 degrees where the apparatus has an added attractive force such that the plumb line of the pendulum is parallel to the axis of rotation of the Earth, not at an angle to the axis. The Coriolis Effect that causes the precession of the plane of swing has no impact on the pendulum swing such that the direction of rotation that opposes the Earth's rotation would be eliminated.  This would result in a rotation of the plane of swing of one day at the latitude that is the same as observed at the poles.  This would not only demonstrate that the Earth turns but would also be an experiment in isolating the Coriolis Effect. David Harty (talk) 11:46, 29 September 2008 (UTC)


 * To compare the Coriolis Effect to the twisting of the pendulum wire, consider a Foucault pendulum experiment where the apparatus is constructed with a floating suspension point that could be imagined to be like a pontoon boat floating over an annular tub. Initially it might be thought that the force from the Coriolis Effect is isolated from the pendulum apparatus such that the precession would be eliminated that is opposite of the Earth's rotation. This would not be a correct interpretation since the Coriolis Effect results in rotation of the plane of swing of the pendulum not the point of suspension. The Coriolis Effect occurs because the mass of the pendulum bob has inertia in the initiated plane of direction (plane of motion) that opposes the change of direction due to the rotation of the Earth.


 * Separately, the Foucault pendulum apparatus allows the suspension wire the freedom to twist and untwist at the suspension point as the Earth turns. At the wire contact point the pendulum wire will twist relative to the contact point and can twist back as the strain is built up in the wire. With a floating suspension point the wire at the connection point will no longer twist or build up strain since the constraint is eliminated. David Harty (talk) 10:46, 9 October 2008 (UTC)

Animations
I changed the first animated figure and caption to more clearly show the fixed plane of oscillation of the pendulum (blue). There were three animations on the Wikimedia site for the animation, and the second one Foucault-rotz.gif, not the first, was the one that best illustrated the case under discussion, namely a Foucault pendulum at the North Pole. CharlesHBennett (talk) 07:25, 2 November 2008 (UTC)


 * You changed animation A [[Image:Foucault-anim.gif|250px|thumb|right|A Animation of a Foucault pendulum, with the rotation rate greatly exaggerated. The green trace shows the path of the pendulum bob over the ground, and the blue trace shows the path in a frame of reference rotating with the plane of the pendulum.]] to B but the reference to north pole and to fixed stars is not correct: Animation of a Foucault pendulum at the North Pole, 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 the inertial reference frame of the fixed stars.


 * The 3 animations (A, B and C) correspond to the historical and geographical position of the pendulum in the Pantheon in Paris (48°52' North). At this latitude, the pendulum is not free as it could be at a pole and it is the reason why its period is bigger than a day. [[Image:Foucault-rotz.gif|250px|thumb|right|B 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.]]


 * I think that the first fixed image is enough to explain the easy situation at the pole.


 * Animation A is better to explain the real phenomena which made and makes the Foucault pendulum so attractive. But in 1851, people visiting the Panthéon were not completely convinced that Earth was rotating in reference to fixed stars. Because of the latitude of Paris, the pendulum wasn't a complete proof of the existence of fixed stars. And Foucault was disappointed. A year after, in 1852, he proposed (but not discovered) the gyroscope which was a real proof.


 * If you want a view from the fixed stars, I designed a third view C from the sun (and its ecliptic plane). [[Image:Foucault-soleil.gif|250px|thumb|right|C Animation of a Foucault pendulum at the Pantheon in Paris (48°52' North), with the earth's rotation rate greatly exaggerated. View from the Sun]]


 * In fact, if you really look close to the animations you will see a stick at the center. And the pendulum is launched at mid from an exact east position. You can follow the shadow of the stick on the ground and it turns quicker than the pendulum plane. On the French wikipedia, the three animations are presented and explained (long caption). Nbrouard (talk) 15:22, 20 November 2008 (UTC).
 * Dear, thank you for your animations. Could you collapse the blue curve into a circular arc as for a simple pendulum, please? Currently the blue curve seems to depict a more complicated trajectory of a conical pendulum's bob. Thanks! fgnievinski (talk) 08:37, 2 July 2023 (UTC)



South point chariot
heya, what does the South point chariot have to do with the Foucault Pendulum? from what I read it seems to demonstrate the curvature of the earth by having the pointer point in the wrong direction if you move along a parallel, and not the rotation of the earth.[goduranus] —Preceding unsigned comment added by 70.79.73.161 (talk) 02:13, 8 February 2008 (UTC)


 * As I understand it the south pointing chariot is mentioned to illustrate the concept of parallel transport. If you would be on a non-rotating planet, and you would travel with a Foucault pendulum, on a circumnavigating journey, then the direction of the plane of swing would develop over time in the same way as the direction in which an idealized "south pointing chariot" would point over time. (Obviously, an actual Foucault pendulum would be messed up if you travel with it, but this is a thought experiment for the purpose of demonstration.)


 * Personally I'm unhappy with the fact that the South pointing chariot example is mentioned, I think it's not worthwile, I think it's more confusing than illuminating. --Cleonis | Talk 23:08, 13 February 2009 (UTC)


 * Quite contrary to the previous comment, I think South pointing chariot is a very illuminating example. Two wheels of the eastbound chariot have to travel along Earth parallels of different lengths (in the N hemisphere the left wheel has to travel smaller distance than the right wheel during circumnavigation), and therefore the chariot has to continuously perform slight left turn correction in the plane tangent to the Earth sphere in order to maintain its eastbound direction of travel. In the absence of this turn correction, the chariot will be slowly rotating to the right, as the left wheel runs ahead of the right wheel in terms of the longitude coordinate on the sphere. This is exactly what happens to the pendulum: in the absence of correcting rotational force around the locally vertical axis, the plane of swing precesses clockwise. --cherkash 12 June 2009 —Preceding unsigned comment added by 192.193.171.219 (talk) 17:01, 12 June 2009 (UTC)


 * Although there are parallels, giving rise in both cases to a sine law, in the end what explains the South pointing chariot example is distinct from what explains the Foucault turning.
 * Some time ago I have created two Java applets, available at the Open source physics repository, that demonstrate the physics underlying the Foucault turning.
 * - Circumnavigating pendulum: a 2D simulation that focuses on an essential aspect of the Foucault pendulum motion.
 * - Foucault pendulum: a 3D simulation of the dynamics of the Foucault turning.
 * (I posted these links on this talk page before, in the section 'the gnuplot animation')
 * The advantage of simulations is that they are interactive; various settings can be adjusted, to see what the effect is. --Cleonis | Talk 19:34, 12 June 2009 (UTC)


 * I've gone ahead and removed the south-pointing chariot example. As mentioned above, the two systems are measuring completely different things.  The Foucault pendulum measures the rotation of the earth, not its curvature, while the chariot measures the curvature of the earth, not its rotation.  Contrary to what was explicitly claimed in the article, a south-pointing chariot behaves identically on a rotating and on a non-rotating planet, unlike the pendulum, while the pendulum would act the same on a planet of any size rotating at the same rate as the earth, unlike the chariot.  The chariot example could only confuse the reader.  (This all assumes a gear-based south-pointing chariot, and ignores the practical impossibility of constructing such a gear system accurate enough to remain oriented after a circumnavigation of the earth.)  50.184.101.91 (talk) 19:05, 30 March 2015 (UTC)

Vandalism
Saw this "The experimental apparatus consists of a cock tall pendulum free to oscillate in any vertical plane." and I don't think 'cock' is a technical term so I removed it. —Preceding unsigned comment added by Lesssthan (talk • contribs) 20:28, 13 February 2009 (UTC)
 * You may purchase a cock tail pendulum here: http://au.alibaba.com/product-image/119178136-Iron-Pendulum-Balanced-iron-cock-Figure.html. Cock is indeed a technical term denoting the male of the bird species; hen denotes the female. Thus, 'peacock' is the male, 'peahen' is the female. You may find references to cocks crowing at dawn in Shakespeare, referring, of course to the mail chicken. The term 'rooster' is relatively recent. Circa 1600, 'roost cock' referred to the male chicken, as in "the roosting bird." That term was shortened to 'roost' circa 1772 because the term 'cock' caused some discomfort among the Puritans; 'rooster' is the noun form of the verb 'roost'. The above statement focuses on the slang, which is inappropriate in a technical article. However, 'cock' referring to the male bird is appropriate, as is stop-cock, to cock a pistol, and part of the governor of a steam engine. Since the sense of the term is part of a sentence referring to a type of pendulum, it is difficult to justify assigning the colloquial slang definition to the term. Perhaps the above removal was made by someone who cannot separate slang from the technical? If the original author had intended to refer not to a type of pendulum, but a penis, then it could be appropriate to change 'cock' to 'penis', however, deleting an entire sentence that describes a scientific experiment performed in the 1850's is the misguided ludicrous act of a neo-Puritan. Good thing the article wasn't about cock feathers on an arrow. Mental discipline is difficult to achieve, it takes practice. Any book referring to Foucult's scientific experiment should be burned in the public square? But I digress.

Removed incorrect animation


I removed the Image:Foucault pendulum animated.gif animation.

It is a whopping 1.05 MB, and its quality does not justify shipping such a humongous file. (In many parts of the world people are dependent on internet connection via plain old telephone line.)

The main problem is that the animation does not represent the motion pattern of the foucault pendulum correctly. The bob in the animation crosses precisely over the midpoint of the swing, and it is not stationary at the extremal points of the swing.

The image shows a schematic view of the actual motion pattern of the pendulum bob. (More precisely: the motion pattern of an idealized pendulum bob, one that moves according to the basic equations of motion.)

Right before the pendulum bob is released it is co-moving with the Earth, and in the idealized case that persists: at each extremum of the swing the pendulum bob is momentarily stationary with respect to the Earth. --Cleonis | Talk 20:40, 11 March 2009 (UTC)


 * Ok, I had originally added the animation based on the quality of the image. If it is not technically accurate, than that is another story. If it was accurate maybe we could have placed a link to it(so as not to impede the people left with dialup). However, I feel we should edit the articles based on quality(as long as they are accessible to the majority). But, if you are saying that the animation is incorrect, then this is a moot point. You must admit it was a great looking animation(it is a featured picture on Wikimedia Commons (Featured pictures) and is considered one of the finest images.). Wacko Jack O   07:17, 12 March 2009 (UTC)


 * Well, the Image:Foucault pendulum animated.gif animation isn't my taste, too flashy, (but that's a matter of taste). The main purpose of that animation, it seems, it to sell itself, or to demonstrate the author's skills, explanation does not seem to be its purpose.


 * Speaking of which, the following animation, that is in the article Image:Foucault-rotz.gif manages to combine the following two properties: it is ugly, and huge in filesize: 372 KB. Despite the huge size it is only a couple of seconds of frames, then it jerks back to the start. In my opinion: to qualify as 'good' an animation must be under 100 KB and it must loop smoothly. --Cleonis | Talk 17:12, 12 March 2009 (UTC)


 * I personally don't think an image needs to be under 100kb to be a quality image. If it is a good image, then use it. That's just my opinion. I would be curious to know the percentage of visitors who come here by dialup as opposed to broadband, etc. Wacko  Jack O   00:27, 13 March 2009 (UTC)


 * When I saw the wrong path of this Image:Foucault pendulum animated.gif, firstly mentioned on this English discussion page by Cleonis (see the archives), I decided to rewrite the mathematics (still on the French page in order to ask Dominique Toussaint alias DemonDeLuxe to change the initial conditions of his integral equations (or to use the proposed solutions) so that the path will show the singular point or cusp which is a crucial, historical and pedagogical point.


 * Unfortunately, Dominique Toussaint (a German young guy who produced probably the most beautiful animations of Wikipedia) was already dead and did not answer me. And the source code of his animation was not available and probably lost forever.


 * Therefore I decided to propose 1, 2 and yet 3 animations, under a GPL license, with latest version of Gnuplot. This latest version permitted gif animations at low cost (small size of the images) but still, I can't easily add a fourth color for the Coriolis acceleration (limitation of current Mediawiki/Wikipedia server when creating thumbs which made Wikipedia servers collapse [ see old discussion with Tim Starling on bugzilla ] ).


 * In fact, what is really missing in my animations is a perception of the very high speed of the rotating Earth (zero at the poles, and 40 000 km per day at the equator) which explains the variation by latitude: a path of the zenith sun spot could be added (in the future) to the 3rd view (from the sun).--Nbrouard (talk) 09:55, 27 March 2009 (UTC)

The gnuplot animation
Hi Nbrouard,

in the previous sections I already gave some reasons for being dissatisfied with the gnuplot animations.

The original is 640x480 pixels. The lines in that animation are single pixel lines. In the article the code specifies a width of 250px. But downscaling an animation is a horrible waste of resources: each frame of the animation must be scaled down individually! And this entire downscaling must be performed again and again, each time the page is viewed. An animation must always be displayed in original resolution. If a animation must be small then it must be manufactured and uploaded in the intended resolution.

It seems to me that animation is too limited to explain the physics. Some months ago I created two Java simulations, using EJS, a tool for generating simulations complete with user interface. These Java simulations are available on two locations: my own website, and in the Open Source Physics repository of featured simulations. I give the links to the OSP pages. - Circumnavigating pendulum: a 2D simulation that focuses on an essential aspect of the Foucault pendulum motion. - Foucault pendulum: a full 3D simulation of the Foucault effect.

The simulations calculate the trajectories by performing numerical analysis of the differential equations.

It is difficult to see how the information that is conveyed by those applets is to be conveyed in an animation.

I have created animations with POV-ray, such as the animations for the Coriolis flow meter article. I can try to create something similar to the animation that DemondeLuxe created, but with cusps (but to save KB's I would use a palet of 16 shades of grey instead of full color) --Cleonis | Talk 23:11, 27 March 2009 (UTC)

Foucault pendulum at the United Nations
I'm rather surprised that the article does not discuss this one at the UN (or did I miss something?): ]. --Ludvikus (talk) 09:22, 23 September 2009 (UTC)


 * And here's a quote of the descriptive text linked above:
 * "A prominent feature of the General Assembly Lobby is the Foucault pendulum, given by the Netherlands to the United Nations in 1955. The Foucault pendulum, named after the French physicist Jean Bernard Leon Foucault, gives visual proof of the rotation of the Earth."


 * "It consists of a gold-plated sphere, partly filled with copper, suspended from the ceiling 75 feet above by a stainless steel wire. A universal joint allows it to swing freely in any direction. An electromagnet under the pendulum counteracts the friction in the air, thus keeping the pendulum swinging uniformly. During the course of a day, the direction in which the pendulum swings appears to change due to the rotation of the Earth. It takes the sphere 36 hours and 45 minutes to complete its cycle."


 * --Ludvikus (talk) 09:30, 23 September 2009 (UTC)

Oscillation dampened by friction?
Currently, the article states: "Air resistance damps the oscillation, so Foucault pendulums in museums often incorporate an electromagnetic or other drive to keep the bob swinging; others are restarted regularly."

What about friction at the pivot point? Doesn't that dampen the oscillation, too? Freddicus (talk) 21:46, 9 February 2010 (UTC)


 * Yes, there is a small amount of friction (and movement) at the pivot, but the energy lost at a well-designed and firmly-supported pivot is small compared to that lost through the effects of air resistance.   D b f i r s   22:01, 9 February 2010 (UTC)


 * Thanks, I didn't know that! Is it worth mentioning what you just said in the article? Freddicus (talk) 16:06, 11 February 2010 (UTC)

Lead paragraph
I noticed the lead length tag at the top of the page, so I extended it just a bit; I didn't feel there was much to summarize without repeating information. What do you folks think? Somnambulent (talk) 16:44, 29 November 2010 (UTC)

Re: Visualization: Foucault vs. Coriolis
This section is complete bogus. Firstly, it's just a bunch of loosely knitted heuristic arguments with little value of actually explaining anything. They are so vague that it's basically impossible to assess if they are right or not, or where they go wrong. More importantly, the only clearly stated point "The apparent rotation of Foucault's pendulum is not due to the Coriolis Effect" is plain wrong. The Foucault rotation can be explained in a number of ways, and the Coriolis effect is one of them. It arises if one chooses the rotating frame of reference given by an earthbound observer, and one considers the corresponding equations of motions. This is explicitly done two sections higher and the calculations clearly show that the term corresponding to the Coriolis force is responsible for the Foucault rotation.

If one chooses an inertial system as a reference system, there is of course no Coriolis force, so from that perspective other effects are responsible. This leads to the "parallel transport" interpretation. If the calculation for parallel transport is carried out in local coordinates given by latitude and longitude the Coriolis force reappears as the Christoffel symbols.

I am removing the section, don't put it back in before actually doing a calculation yourself. ShanRen (talk) 19:51, 15 April 2011 (UTC)

Where's the linkage?
The reason the actions of the Foucault pendulum took a long time to be noticed is that the way the pendulum is fastened to its anchorage up top has got to enable free movement over planes of swing of 360 degrees of play. A stone wrapped in a rope tied to a tree limb will lose the effect due to friction in the rope and the knot up top. Thus, the whole key to such a pendulum is the linkage that goes up top. I turned to this page to see the drawing that has appeared at the pendulums in museums that I have seen, but it isn't here. 4.154.253.192 (talk) 21:33, 20 June 2011 (UTC)


 * What kind of linkage are you thinking of? It should suffice if the wire is just made to pass tightly through a rigidly-clamped pinhole-aperture. That will prevent the asymmetric friction which you describe. (You could also add a fishing line swivel, if you were concerned with minimising oscillating twisting/torsion, but that would be unlikely to affect the pendulum operation.) Cesiumfrog (talk) 04:09, 16 August 2011 (UTC)

Was the South Pole pendulum asiderial day period?
Did the South Pole pendulum rotate with a periond of 24 hrs or a period of 23.93 hrs? see http://en.wikipedia.org/wiki/Foucault_pendulum#Foucault_pendulums_around_the_world D c weber (talk) 17:13, 20 December 2012 (UTC)

First section heading in italics
Why is the first section heading, "Original Foucault pendulum", in italics?--Rockfang (talk) 06:17, 18 September 2013 (UTC)

Last paragraph needs a look
The last paragraph seems strikingly out of keeping with the rest of the article. Could someone familiar with the article take a look? The paragraph needs a little copyediting, but most of all, what's with the editorializing statement Therefore, they were compelled to complete this tribute to science? The therefore makes no sense, as the statement isn't drawing a logical conclusion from what came before. Sounds a bit like an auto-translation. The paragraph also has no citation. Cynwolfe (talk) 12:32, 18 September 2013 (UTC)

BIG confusion in this article
and it also says that For example, a Foucault pendulum at 30° south latitude, viewed from above by an earthbound observer, rotates counterclockwise 360° in two days.
 * The article says that The plane of the pendulum's swing rotated clockwise 11° per hour, making a full circle in 32.7 hours

'''Neither of the two sentences is right. The article should indicate:'''
 * ''The center of circle on which is moving the pendulum moves to the right 15º per hour (in the Northern Hemisphere) since it is located on a parallel of latitude which gives a complete dayly turn in 24 hours. As a consequence, any point on that circle will turn twice everyday: one turn around the parallel of latitude and another turn around the center of the same circle. If movement of pendulum throw 24 pins around the circle (15º distance from one another), all of them will fall in 12 hours: 12 pins each half circle. Pins are displaced by pendulum to the left, that is, counterclockwise, on the Northern hemisphere (in both ways) and to the right (clockwise) in the souther hemisphere, also in both ways. --Fev (talk) • (contribs)  —Preceding undated comment added 03:47, 7 February 2014 (UTC)


 * Are you sure that the confusion is not yours? Have you checked your facts with scientific papers?    D b f i r s   09:29, 7 February 2014 (UTC)

A very simple geometric demonstration
To explain the behaviour of the Foucault pendulum there is no need to introduce and analyze mysterious fictitious forces : one must only observe that during a time interval as short as you like, the swinging plane's direction can be considered fixed relatively to the stars, but its trace on the observation table moves because that table and thus the South engraved mark rotates (in absolute space) under the pendulum with the constant angular speed (ω sinλ) around the instantaneous but mobile position of the vertical n(t) at the location of the pendulum. In the northern hemisphere the South mark rotates (unseen by the Earthbound observer) counterclockwise, while during a short time span the pendulum trace stays stationary in absolute space. Thus the Earthbound observer sees the trace moving clockwise with the above mentioned angular speed. And what is important to note is the fact that in his Earthbound reference system these angular variations can be arithmetically added, that is integrated. Thus the Foucault pendulum law is explained (of course I exclude here the more sophisticated elliptic moves). One must add that the curvatures of the trace seen in the animations are enormously exxagerated. By the way a strictly plane trajectory in absolute space is necessarily curved in the rotating system. Chessfan (talk) 10:11, 13 February 2014 (UTC)

Images
I have just added (readded ?) a nice animation that captures the essence of the Foucault pendulum - I know there have been issues with this before (see section 8 above), but I think the animation grabs the reader's attention. Also, there are 4 images pertaining to the pendulum at the Pantheon - overkill ? Although there is historical significance here, I think some of the images should be removed (1 or 2 are probably enough). I suggest removing the second and third ones; the second one just shows the bob, the third one information about repairs. The first one should be kept as it shows the whole pendulum in all it's glory, and the last one should be kept as it's a nice animation with details. Perhaps also removal of the Ranchi image would be appropriate (it doesn't add anything to the article); the same may be said of the California image. Thoughts ? MPatel (talk•contribs) 12:53, 12 July 2014 (UTC)

''It was difficult to make the pendulum swing in a plane instead of an ellipse. After several attempts with various techniques of holding the bob and dropping it we always got some kind of ellipse instead of a plane. This adds to our error because it is more difficult to locate and mark the pendulum arc’s apex. A way to do it is to suspended the bob by tying it off with a piece of string and letting it settle, then burn through the string. The bob would then drop without any outside force and swing in a plane. Since it is against the Antarctica Treaty to have any open flames at the South Pole we could not do this. After much practice Mike Town got very adept at dropping the bob so that it arced in a plane.'' Unfortunately they estimated that an open flame wasn't allowed at the place where the pendulum was launched. This strange ban doesn't seem to exist in the antartic treaty but is a general fire prevention, may be because of the altitude or because the air is dry. Quoting a fire plan of a South Pole Station an open flame is everyone's responsibility:
 * The well-known image of User:DemonDeLuxe (he won a price) doesn't correspond to the history of the Foucault pendulum. The movement described in the figure cannot be obtained when the pendulum is released with a null speed. Foucault waited (in front of the public, see this page or that page) until the oscillations of the cable vanish before releasing the ball carefully by burning a rope that held the ball (see photo). Many people were still reluctant to believe in the rotation of the earth and the discussions were not over for a while... That is the reason, why the initial conditions of the release are so important and highly discussed in this Talk page.
 * When I asked Dominique Toussaint, some years ago, to modify his nice drawing, he was unfortunately dead. It would have been easy for him to modify the initial conditions of the ball release. His drawing corresponds unfortunately both to a release of a pendulum in the South hemisphere (which was not his intention because the Pantheon is in the North hemisphere) and to a release with an initial speed from the center, using a rocket or something like that. That is the reason why previous contributors to this page removed this nice image. --Nbrouard (talk) 14:13, 20 August 2014 (UTC)
 * Finally, I found a public domain cover of a famous magazine "Le Petit Parisien" for the fiftieth anniversary, in 1902, of the original demonstration of Foucault. It shows how the rope was burned (see detail of the launch at the fiftieth anniversary in 1902) Le petit Parisien illustre 2nov1902.jpg. I added in the main page, near the description of the launch. --Nbrouard (talk) 18:09, 20 August 2014 (UTC)
 * I also looked at an article describing the experiment of pendulum at the South Pole in 2001. We can read how difficult it was to launch the bob:
 * ''Fire prevention at the South Pole is everyone's responsibility. Some guidelines No open flames, space heaters, or electric blankets are allowed except in authorized areas. Smoking is permitted outside and in designated smoking areas only...
 * I hope I was convincing and that you will admit the importance of initial conditions as well as the shape of the path on the ground.--Nbrouard (talk) 09:07, 22 August 2014 (UTC)

I've rejigged the location of some images and taken 2 images out (2nd and 3rd Pantheon ones referred to above) to see what the article now looks like. Comments ? MPatel (talk•contribs) 13:20, 12 July 2014 (UTC)

Question about the explanation beneath the image at the Cal Sci Center: It says "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." I was under the impression the explanation is the exact opposite.. as in "The Earth's rotation causes the building to rotate around the pendulum while the trajectory of the pendulum remains unchanged" — Preceding unsigned comment added by 23.118.9.41 (talk) 23:10, 29 July 2015 (UTC)

Some data
According the given formula, the numbers for rotation rate (in degrees per hour) and precession period (in days) are now accurate to one decimal place. The previous version seems to have calculated the rotation rate to the nearest degree, and then introduced some roundoff error by using that value to compute the period. Of course, it would be better to use an original measurement instead of a computed ideal value, but it is what it is for now. Deacon Vorbis (talk) 03:34, 9 February 2017 (UTC)

External links modified
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New GIF animation of a pendulum at the north pole
This new GIF might be of interest here. Authors may feel free to insert it. --Modalanalytiker (talk) 14:31, 4 December 2018 (UTC) --Modalanalytiker (talk) 09:58, 5 December 2018 (UTC)


 * FoucaultGlobusAnima.gif

... it doesn't seem to work as a thumbnail ... Purgy (talk) 15:52, 4 December 2018 (UTC)


 * If I click into the image your edit has generated -  it moves. Is that less than you expect? --Modalanalytiker (talk) 19:25, 4 December 2018 (UTC)


 * Yes, I expect it to move, without turning fullscreen. I would like very much to start/stop animations when clicking on them, but them only moving in fullscreen is unsatisfactory to me. Purgy (talk) 06:25, 5 December 2018 (UTC)


 * Would you be so kind to post a link to an animation example fully complying with your specification? --Modalanalytiker (talk) 09:49, 5 December 2018 (UTC)


 * I am terribly sorry that I know of none. As I said, it is a desire of mine, I should have said that I do not know of fulfillment. Clicking just makes pics fullscreen. There are thumbs that move (partly wrongly), and can't be stopped (ancient curse: May your tags blink in eternity!), there are some that don't move in thumb (only in full screen), but I know of no controllable ones. I feel no desire to implant this new pic, I'd rather remove the wrongly moving one. :( Purgy (talk) 10:36, 5 December 2018 (UTC)


 * As you probably read in the main page or in this talk page, the main scientific interest of the Foucault's pendulum resides in the initial conditions of the launch. Also, having a launch at the pole would have been of no interest for Foucault because the period is of 24 hours.


 * At last, you can find an animated thumbnail above as well as in the German wiki https://de.wikipedia.org/w/index.php?title=Foucaultsches_Pendel&oldid=181164112 just before you replaced the original animation mini|Veranschaulichung der Pendelbahn with yours without any warn and argument. I am the author of this animation, but the link to the German wikipedia has been added by someone else some years ago. While reading the German page and its talk page, I haven't seen any major difference with the Mathematics of the original French wikipedia. But if so, you can modify the Gnuplot source code (which is provided on [Commons]) and replace the dome of the Pantheon in Paris with the globe, but please place it at a latitude for which the Foucault experiment has a scientific sense. --Nbrouard (talk) 13:26, 5 December 2018 (UTC)

New version
An extended version - of course not for implementing $$-$$  only for executing the jus primae censurae delentis - the most exciting zest of Wikipedia upper class great-authors.--Modalanalytiker (talk) 12:33, 29 December 2018 (UTC)

1 meter foucault pendulum video and how-to
https://www.youtube.com/watch?v=YjP-MLXdGYY has a 12 hour video showing the Foucault rotation of a 1 meter driven pendulum. That page also has links to pages showing how it is built, and a variation on the explanation of the rotation. I would appreciate it if a link could be added to this page.

John Dooley 2601:985:104:4470:14B0:697F:5CDA:5BFE (talk) jwdooley@aol.com — Preceding undated comment added 21:37, 18 December 2020 (UTC)

Does swing really matter when a similar result is obtained from a static Foucault pendulum?
It is said that a Foucault pendulum is not restricted to remain in a single defined linear direction or it can swing in any direction in the vertical. Earth’s rotation can’t force the bob to swivel therefore let the Foucault pendulum be at rest instead of swinging back and forth.

Attached or fixed the laser pointer to the great circle of the bob of the said pendulum. The laser beam shines perpendicular to the suspend wire of the pendulum. Earth rotates beneath the bob when the Foucault pendulum is at rest as there is a relative motion exist between them. This means the laser shines in a specific direction in a fixed plane while the earth and the building the pendulum resides rotates about the said plane in which a bob rest. Even a simple mark on the aforementioned bob (not on points through which its mg is passed) is enough to notice the rotation of the earth with the passage of time.39.32.106.21 (talk) 10:10, 30 April 2021 (UTC)eek

== Wherever you put it, Foucault's Pendulum swings from a motionless point while the earth rotates beneath it. Every point of the universe is a fixed point: all you have to do is hang the Pendulum from it ==

I have several problems with this page,

This needs to be said before the first example, not afterwards. "the amount of time that it takes for the pendulum to make one full rotation (with respect to its surroundings) is equal to one sidereal day (23.93 hours) divided by the sine of the latitude of its location. 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 precesses relative to Earth, but more slowly than at the pole, proportional to the sine of the latitude..."

Secondly, people aren't content with amateur footage of the Parthenon? We might need a twelve hour video to explain precession?

There are several far more useful depictions on the wiki commons page.

https://commons.wikimedia.org/wiki/Category:Foucault_pendulums

I humbly request this page gets submitted to an authority that will rigorously edit this page.

This surely has to one of the most well known scientific examples of the heliocentric universe. And it seems impossible to read by the average reader, and the simple Wikipedia offers no explanation. 49.185.200.59 (talk) 04:16, 18 May 2022 (UTC)


 * There is no authority. Why don't you try implementing the changes you describe? WP:BEBOLD CyreJ (talk) 06:48, 18 May 2022 (UTC)

Choice of latitude variable
The second section of the article ("Original Foucault pendulum") uses $$\phi$$ for the latitude variable, but the remainder of the article after that uses $$\varphi$$. Are these representing the same quantity? If so, I suggest they should use the same variable. Is there a typical choice for this variable name in the literature? The Latitude article seems to use $$\phi$$. —&#8288;&#8202;&#8288;BarrelProof (talk) 22:34, 25 September 2022 (UTC)

Clockwise vs Counter clockwise
In article "rotating clockwise approximately 11.3° per hour." - is this correct? — Preceding unsigned comment added by 146.66.167.197 (talk) 05:36, 25 November 2022 (UTC)


 * Yes, in the northern hemisphere the pendulum swings clockwise. Nbrouard (talk) 19:04, 25 November 2022 (UTC)

Note, this could be an evidence, that model of "Flat Earth" is wrong. How their model explains that Foucault pendulum moves in different direction in Krakow and in Sydney?

"perpetuated for twenty-four hours ... an entire revolution"
if the oscillations could be perpetuated for twenty-four hours, the trace of their plane would then execute an entire revolution Then the article describes how, except at the poles, the pendulum executes only part of a revolution in 24 hours.

Did Foucalt get this wrong? Is the restriction missing by selective quotation? It seems to be misleading, and contrary and confusing. Without qualification, it's a bad place to start. 1.159.36.184 (talk) 11:07, 28 June 2023 (UTC)


 * The pendulum is at the North Pole. Before the quote, Foucault wrote "l’observateur se transporte au pôle pour y établir un pendule réduit à sa plus grande simplicité". Ceinturion (talk) 14:32, 28 June 2023 (UTC)

Animated picture Foucault pendulum animated is misleading
I understand that picture "Foucault pendulum animated" is not real but it is misleading from my point of view. Pendulum doesn't move so fast in real observation, changes of direction are much smaller... 213.29.28.253 (talk) 09:18, 5 May 2024 (UTC) You are right and this is the reason why the caption starts with: « Animation of a Foucault pendulum on the northern hemisphere, with the Earth's rotation rate and amplitude greatly exaggerated. »


 * My note was about File:Foucault pendulum animated.gif. The real observation is much different... 213.29.28.253 (talk) 22:07, 7 May 2024 (UTC)