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When I was thinking of Foucault's pendulum , this question was always bugging me. If we are all rotating with the same speed in one reference frame as the surface of earth with the pendulum , then the pendulum as demonstrated by Foucault must have gone through the same place over and over again. Like a line going in the same path but only the earth under it rotates for which we don't find any rotation!

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I tried to check other stack questions Like this but however , it does not address the pendulum being in contact with earth but just talked about atmosphere's connection to it. Due to this I still don't understand Foucalt's pendulum. How did the creator demonstrate it in Paris?

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    $\begingroup$ The pendulum is not in contact to earth it is suspended on a point, which you can consider the center of rotation. There are so many science museums where you can see the Experiment, it is not too difficult to do it even at home for a not so long time, also a simulation on a turning chair will show the effect. $\endgroup$
    – trula
    Mar 19, 2023 at 16:41
  • $\begingroup$ the thing is the point where the pendulum is suspended from , lets take the building of a museum right is in contact with earth right! hence if a change is there is reflected to the swing , this was and is my main concern , how did foucault perform this in the first place ? $\endgroup$
    – Naveen V
    Mar 19, 2023 at 17:22
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    $\begingroup$ There is a youtube video that opens with a shot of the rod-in-the-chuck-of-a-lathe observation that was instrumental in Foucault recognizing that a large pendulum can make it visible to the naked eye that the Earth is rotating. Initially the lathe is not turning, the rod is swinging vertically. Then the chuck starts turning, and the plane of swing does not go along with that; the plane of swing remains vertical. The momentum of the swinging motion has an existence of its own, independent of the orientation of the physical rod. $\endgroup$
    – Cleonis
    Mar 19, 2023 at 20:28

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If we are all rotating with the same speed in one reference frame as the surface of earth with the pendulum.

We are all rotating with the same speed in one reference frame as the surface of the earth. But the pendulum isn't. That's why Foucault's pendulum works.

As the pendulum swings, from it's perspective it is swinging freely in an inertial reference frame. While the pendulum bob may be constrained to rotate with the local rotation of the earth*, the upper end of the pendulum is suspended on a mount that lets the cable pivot around a point in any traverse direction. So the swing of the pendulum is free to do it's thing -- and what it will do is to follow a trajectory that does not rotate in its inertial frame.

Basically, the pendulum is across a vertical axis, and does not rotate in inertial space about that axis. So it is insensitive to rotation in the ground underneath it which are parallel to that axis**.

In essence, this makes the Foucault pendulum into a really big, heavy, and awkward version of a vibrating-arm gyroscope -- and we know vibrating-arm gyroscopes work, because that's the basic technology the MEMS gyroscopes you find in cell phones***.


* Depending on how it's suspended, but I think mechanical sanity demands that it be suspended thus.

** Which means that how fast a Foucault pendulum's axis appears to rotate with respect to the earth is dependent on your longitude -- if you're at a pole, then it'll complete one rotation in 24 hours. If you're at the equator, then to a first order approximation it won't rotate it all -- although, it'll probably actually wander a little bit. If you're somewhere in between -- it'll be somewhere in between.

*** There are also quartz MEMS gyroscopes that are orders of magnitude bigger than cell-phone MEMS gyroscopes (but orders of magnitude smaller than the Foucault pendulum you may find at your local science museum).

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  • $\begingroup$ Upon further reading your answer and the comment , what I get is the rope-bob's motion is undisturbed even when the surroundings are in rotation , being a point from which it's suspended can't do much to change the trajectory of the object to go with the rotation of earth, this is why it works , am I correct here? $\endgroup$
    – Naveen V
    Mar 19, 2023 at 18:46
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    $\begingroup$ Yes. I've edited my answer to (hopefully) clarify this point. $\endgroup$
    – TimWescott
    Mar 19, 2023 at 19:49
  • $\begingroup$ There is still some ambiguitity in this answer. Here's the thing: for a Foucault pendulum located at the latitude of Paris: the period of veering of the plane of oscillation is 32 hours. That implies: if at t=0 the plane of swing is north-south then after 24 hours (Earth back in the same orientation), the plane of swing is east-west. That is, the pendulum bob has exchanged momentum with the Earth. To see how that happens: imagine an asteroid with a giant Foucault pendulum erected on it. Make the mass of the pendulum bob 10 % of the mass of the asteroid. That pendulum bob wil exchange momentum. $\endgroup$
    – Cleonis
    Dec 28, 2023 at 22:15
  • $\begingroup$ [continued] In the case of our usual Foucault pendulum: the effect on the Earth is negligable of course, but the effect on the motion of the pendulum is significant. The fact that suspension point is circumnavigating the Earth's axis is a major factor. My point is: the veering of the plane of swing of the Foucault pendulum is more subtle and more interesting than given credit for. $\endgroup$
    – Cleonis
    Dec 28, 2023 at 22:15

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