Talk:Foucault pendulum

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

  

  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.

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).

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 Nbrouard, 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)

New GIF animation of a pendulum at the north pole

Foucault 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)

Foucault pendulum at the north pole

... 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

Six identical pendulums during six hours

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

The Foucault pendulum rotation still happens even if the pendulum is not swinging at all. It's just difficult to measure. The vertical axis rotates by 360 degrees every day. The pendulum bob is retarded by inertia, and rotates at a slower rate. That is a non-oscillating Foucault pendulum. ~2026-21269-85 (talk) 00:43, 18 May 2026 (UTC)

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 $\phi$. —⁠ ⁠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)

wrong perspective

"A long and heavy pendulum suspended from the high roof above a circular area was monitored over an extended time period, showing that its plane of oscillation rotated." This is the wrong perspective. The whole phenomenon is due to the fact that the plane of oscillation remains FIXED. It is the EARTH that rotated. Kontribuanto (talk) 16:22, 21 September 2024 (UTC)

I have made some changes to the first paragraph in the lead. Dolphin (t) 22:43, 21 September 2024 (UTC)

Actually, except for the North / South pole case, the plane of oscillation does not remain fixed. ~2026-21269-85 (talk) 00:47, 18 May 2026 (UTC)

Accessibility - Animations

One or more animations in this article fail Wikipedia accessibility standards. Wikipedia:Manual of Style/Accessibility#Animations which says: "To be accessible, an animation (GIF – Graphics Interchange Format) should either: Not exceed a duration of five seconds (which results in making it a purely decorative element)[12] or Be equipped with control functions (stop, pause, play)[13]"

File:Foucault pendulum animated.gif is particularly disturbing to people with visual problems.

Humpster (talk) 19:04, 12 April 2025 (UTC)

I put up the one from the COSI museum. Is it OK? It works for me. Bubba73 ^{You talkin' to me?} 19:47, 12 April 2025 (UTC)

That one works as it should. The biggest problem is the fast moving one later. It has a caption which seems to invalidate it. However, it can't be deleted without examining the text, something which I can't do. Humpster (talk) 20:36, 12 April 2025 (UTC)

Coriolis Force

Coriolis Force makes the Foucault pendulum trace a semi-elliptic path. This is normally limited by a collar. Note that equivalent devices (such a laser gyroscopes) demonstrate the same precession as Foucault pendulums, even though they are not subject to Coriolis forces. ~2026-21269-85 (talk) 01:01, 18 May 2026 (UTC)

The Coriolis force is a pseudo-force (or fictitious force) that is only evident in certain non-inertial frames of reference such as the rotating frame of reference defined by the surface of the Earth near the point at which the observations are being made. When observed from a truly inertial frame of reference there is no Coriolis force so it is incorrect to say that the Coriolis force “makes” a pendulum do something.

Fictitious forces are not forces for the purposes of Newton’s laws of motion; that is why they are described as fictitious. When we make observations in a non-inertial frame of reference we see things (such as centrifugal force) that aren’t really there - they are fictitious forces. The best strategy is to define a convenient inertial frame of reference and make observations in that frame because there won’t be any fictitious forces. Dolphin (t) 11:20, 18 May 2026 (UTC)