Foucault pendulum(en.wikipedia.org)
en.wikipedia.org
Foucault pendulum
https://en.wikipedia.org/wiki/Foucault_pendulum
36 comments
Here's the intuition that clicked for me, similar to the above but with a different twist at the end.
Imagine a large flat parking lot, and drive around the parking lot in a circle. Say you have a small pendulum swinging freely, suspended in your car. If you drive the full 360 degrees, the pendulum will appear from the reference frame of the inside of the car to have rotated a full 360 degrees. (Let's say that you are driving fast enough to render the rotation of the earth, the latitude of the parking lot, etc. negligible.)
Whatever fraction of the circle you drive, the pendulum will appear to rotate that same fraction as viewed from inside the car.
Now, here is the fun part. Imagine that you are driving at some fixed latitude on a large sphere. Create a big cone that is just tangent to the sphere on your path. What happens if you drive the entire distance and return to your starting point?
Cut the cone in a vertical straight line starting at its apex, and then flatten out the cone. It will form a flat circle, but with a pie slice removed.
If you had driven the perimeter of this partial circle in the parking lot, you would see that the pendulum only rotated part-way around. The same thing will happen if you drive the full distance around the sphere at the corresponding latitude.
Imagine a large flat parking lot, and drive around the parking lot in a circle. Say you have a small pendulum swinging freely, suspended in your car. If you drive the full 360 degrees, the pendulum will appear from the reference frame of the inside of the car to have rotated a full 360 degrees. (Let's say that you are driving fast enough to render the rotation of the earth, the latitude of the parking lot, etc. negligible.)
Whatever fraction of the circle you drive, the pendulum will appear to rotate that same fraction as viewed from inside the car.
Now, here is the fun part. Imagine that you are driving at some fixed latitude on a large sphere. Create a big cone that is just tangent to the sphere on your path. What happens if you drive the entire distance and return to your starting point?
Cut the cone in a vertical straight line starting at its apex, and then flatten out the cone. It will form a flat circle, but with a pie slice removed.
If you had driven the perimeter of this partial circle in the parking lot, you would see that the pendulum only rotated part-way around. The same thing will happen if you drive the full distance around the sphere at the corresponding latitude.
I had heard it explained explained that way as well. Made sense then and now.
Not to digress, but IF the earth was stationary and everything rotated around it, can you think of a mechanism to explain the pendulums behavior? (Could be ether, or some medieval conception of ptolemic shells, you name it... but it has to be consistent and sort of reasonable sounding.)
Not to digress, but IF the earth was stationary and everything rotated around it, can you think of a mechanism to explain the pendulums behavior? (Could be ether, or some medieval conception of ptolemic shells, you name it... but it has to be consistent and sort of reasonable sounding.)
This would make for a great 3blue1brown visualization.
This is a very good intuitive explanation.
For a quantitative explanation one can make use of the fact that angular velocities or infinitesimal rotations compose like vectors. Earth has an angular velocity that is parallel to its radius to the North pole. When you look at the movent of the surface of the Earth around an arbitrary point, then you can decompose this angular momentum to parallel-to-radius and parallel-to-surface components. The former describes how fast Earth's surface "twists", the latter describes how fast it tilts under your feet. The former is the relevant component for describing the pendulum.
Interestingly this angular-momentum approach has a deeper connection to your car analogy. It can be used to solve the following problem: The Little Prince buys a little car that can turn around on radius r on Earths surface. He brings this car to his home planet, which has radius R. On what radius can this same car turn around on this planet?
For a quantitative explanation one can make use of the fact that angular velocities or infinitesimal rotations compose like vectors. Earth has an angular velocity that is parallel to its radius to the North pole. When you look at the movent of the surface of the Earth around an arbitrary point, then you can decompose this angular momentum to parallel-to-radius and parallel-to-surface components. The former describes how fast Earth's surface "twists", the latter describes how fast it tilts under your feet. The former is the relevant component for describing the pendulum.
Interestingly this angular-momentum approach has a deeper connection to your car analogy. It can be used to solve the following problem: The Little Prince buys a little car that can turn around on radius r on Earths surface. He brings this car to his home planet, which has radius R. On what radius can this same car turn around on this planet?
Thank you! I live in Boston and am a frequent visitor to the Museum of Science, which has a Foucault pendulum. I never truly grasped the explanation until reading your post.
Thanks. I found that explanation a long time ago in some remote corner of the internet... some Japanese website about Transformers and Decipticons as I recall.
Ages ago -- when the Internet was young -- I tried to put the explanation in the Foucaults article on Wikipedia... it lasted about 30 minutes before getting deleted and replaced with the usual trig stuff.
Ages ago -- when the Internet was young -- I tried to put the explanation in the Foucaults article on Wikipedia... it lasted about 30 minutes before getting deleted and replaced with the usual trig stuff.
> lasted about 30 minutes before getting deleted and replaced
My one and only attempt to edit Wikipedia was to redact a statement on the article about the Semantic Web that had recently been changed to note that someone named Dr. Foch was attempting to weaponize the semantic web in support of a Chinese takeover of the world. My edit was immediately removed for not having a valid reference...nevermind that the original note didn't either.
My one and only attempt to edit Wikipedia was to redact a statement on the article about the Semantic Web that had recently been changed to note that someone named Dr. Foch was attempting to weaponize the semantic web in support of a Chinese takeover of the world. My edit was immediately removed for not having a valid reference...nevermind that the original note didn't either.
That's very good. There are a lot of things that sound simple but when you take a closer look suddenly a lot of questions come up. Examples would be this pendulum, aircraft wings or gravity assists of interplanetary probes.
The Foucault Pendulum is on my list of three dead-simple machines that prove science is real.
(1) Using a soup can and some string to measure radiation: https://en.wikipedia.org/wiki/Kearny_fallout_meter
(2) Measuring the force of gravity, and thereby weighing the earth, using a tuna can and some other string. http://www.fourmilab.ch/gravitation/foobar/
(3) Using a string and a bowling ball prove the earth is round without going outside. https://en.wikipedia.org/wiki/Foucault_pendulum
(1) Using a soup can and some string to measure radiation: https://en.wikipedia.org/wiki/Kearny_fallout_meter
(2) Measuring the force of gravity, and thereby weighing the earth, using a tuna can and some other string. http://www.fourmilab.ch/gravitation/foobar/
(3) Using a string and a bowling ball prove the earth is round without going outside. https://en.wikipedia.org/wiki/Foucault_pendulum
I didn't know about Cresson_Kearny [1] until this but he was pretty great. He reminds me of a cold war Macgyver-like survivalist with a number of interesting gadgets [2]
[1] https://en.wikipedia.org/wiki/Cresson_Kearny
[2] https://en.wikipedia.org/wiki/Kearny_air_pump
[1] https://en.wikipedia.org/wiki/Cresson_Kearny
[2] https://en.wikipedia.org/wiki/Kearny_air_pump
The one at BYU has signs around it saying something like "Warning! 10,000 ohms! Do not touch!" I guess the thinking is that those who don't know what ohms are will think it's dangerous and those that do will have enough respect for physics to not disturb the pendulum.
Relatively interesting: https://en.wikipedia.org/wiki/Allais_effect
[deleted]
TIL the smithsonian removed it's Foucault pendulum in 1998 (right about when I moved away from the DC area). It was about 15 meters long and quite impressive; they had little pins setup that it would knock down, so you could look at when you arrived in the museum and see the difference when you left.
If you’re ever in the Bay, the California Academy of Sciences has one (although it’s probably one of the more boring exhibits there).
The Oregon Convention Center has one, watched it every O'Reilly Open Source Conference that was in Portland.
https://www.youtube.com/watch?v=-p7P0DQvp0g
https://www.youtube.com/watch?v=-p7P0DQvp0g
Find one near you! https://en.wikipedia.org/wiki/List_of_Foucault_pendulums
I'm surprised to see Fermi National Accelerator Laboratory listed still. When I last visited Wilson Hall which must have been nearly a decade ago now, the pendulum had been removed. If memory serves it happened after the cable snapped from wear and they decided to just get rid of it.
This [0] post claims they removed it in 2010.
It was kind of mesmerizing to watch back in the day, Wilson Hall is a tall building with an open center, it made for a great Foucault Pendulum.
[0] https://www.vofoundation.org/blog/cabinet-physics-riding-alo...
This [0] post claims they removed it in 2010.
It was kind of mesmerizing to watch back in the day, Wilson Hall is a tall building with an open center, it made for a great Foucault Pendulum.
[0] https://www.vofoundation.org/blog/cabinet-physics-riding-alo...
I've always wondered, are there bots that just post these interesting wikipedia articles periodically? It seems like twice a week or so a random wikipedia article is trending.
I posted my WiFi Coax article because it confused me at first.
No. No! This isn't named after the philosopher Foucault
> The pendulum was introduced in 1851 and was the first experiment to give simple, direct evidence of the earth's rotation.
The existence of the day-night cycle should have sufficed.
The existence of the day-night cycle should have sufficed.
That doesn’t tell you whether the earth rotates or the sun revolves around the earth.
Yes. People have been taught that the earth revolves around the sun, and sometimes we use it as a way to be smug about how much smarter we are than the ancients. But schools do a huge disservice to students by not showing them that there's not in fact any way to know this from the information the ancients had available to them. About all you can infer from the way the sun changes position in the sky is that some kind of movement is happening. Because the earth feels solid under your feet you might assume that only the sun, planets, and stars are moving. This is valid according to Occam's Razor.
Indeed for hundreds of years western astronomers predicted the locations of the planets using epicycles and not by calculating orbits assuming a heliocentric system. And it worked! Beautifully! The earth-centric model has excellent predictive power. It explained everything the ancients were aware of.
This is all as a lesson in both humility and in recognizing that our ancestors were not stupid or lacking reason. They just didn't have the tools we have. And for all that the heliocentric seems obvious, remember that it is only obvious because we have been taught it. Our ancestors had been taught an earth-centric model instead, and it was obvious to them.
Indeed for hundreds of years western astronomers predicted the locations of the planets using epicycles and not by calculating orbits assuming a heliocentric system. And it worked! Beautifully! The earth-centric model has excellent predictive power. It explained everything the ancients were aware of.
This is all as a lesson in both humility and in recognizing that our ancestors were not stupid or lacking reason. They just didn't have the tools we have. And for all that the heliocentric seems obvious, remember that it is only obvious because we have been taught it. Our ancestors had been taught an earth-centric model instead, and it was obvious to them.
They certainly could and in fact did.
https://en.wikipedia.org/wiki/Heliocentrism#Aristarchus_of_S...
https://en.wikipedia.org/wiki/Heliocentrism#Aristarchus_of_S...
Did Aristarchus of Samos develop a model that made any predictions that could be verified? I think that the ancients thinking about heliocentrism were mostly contemplating it as philosophy. The section you linked doesn't say anything about evidence for heliocentrism, which is what 'jschwartzi is saying was lacking.
Stuff like parallax and Foucault's pendulum isn't obvious until it's already been seen, and AFAIK wasn't investigated until the 17th century.
Stuff like parallax and Foucault's pendulum isn't obvious until it's already been seen, and AFAIK wasn't investigated until the 17th century.
To turn that on its head, it's a wonderful teaching moment to ask a room full of smart students to try and prove (or even convincingly argue) that the Earth moves around the sun. A great way to get people to examine their assumptions and look afresh at the world around them.
As you say, it is indeed very hard to do, which is a good part of the reason why even when Copernicus published his heliocentric model (not a proof, but a new mathematical model) his ideas took decades to become mainstream. If you have a rudimentary telescope / binoculars and know to look, then you can observe that Venus has phases and use that as a basis for argument (as Galileo did), but even then, it's perfectly possible to cook up special models where Venus has phases and the earth is still stationary (see https://en.m.wikipedia.org/wiki/Tychonic_system).
As you say, it is indeed very hard to do, which is a good part of the reason why even when Copernicus published his heliocentric model (not a proof, but a new mathematical model) his ideas took decades to become mainstream. If you have a rudimentary telescope / binoculars and know to look, then you can observe that Venus has phases and use that as a basis for argument (as Galileo did), but even then, it's perfectly possible to cook up special models where Venus has phases and the earth is still stationary (see https://en.m.wikipedia.org/wiki/Tychonic_system).
[deleted]
In addition to sibling comments, we should note that not all observations are experiments. There is a distinct difference between experiment and mere observation: In an experiment, we are carrying out a repeatable recipe in order to try to falsify a hypothesis. We are not merely theory-crafting, working to explain what we see, but we are trying to disprove what we have theorized.
> In an experiment, we are carrying out a repeatable recipe in order to try to falsify a hypothesis. We are not merely theory-crafting, working to explain what we see, but we are trying to disprove what we have theorized.
Actually, no. Not sure where you got the idea that an experiment has to falsify a hypothesis.
Actually, no. Not sure where you got the idea that an experiment has to falsify a hypothesis.
And to clarify, observation is as important as experiment, because observation gives us new ideas for experiments. Collecting anecdotes and making observations is as important as designing experiments. You can't really be a scientist if you don't pay attention to the natural world.
The pendulum shows you the net rotation of the pendulum about the Earth's axis of rotation, the rotation of the Earth about the Sun, the Sun about the center of the Milky Way, the Milky Way about the gravitational center of our local cluster, etc., etc.
Having not known, I think I would have strongly guessed that the rotation of the Earth about its own axis would be by far the dominant factor, but it's still good to measure.
Having not known, I think I would have strongly guessed that the rotation of the Earth about its own axis would be by far the dominant factor, but it's still good to measure.
I could picture what was happening with the pendulum at the Norh Pole... earth rotates under the pivot point every 24 hours. And, I understand what happened st the Equator... no effect on the pendulum as nothing is rotating beneath it.
But, at points in between, it was hard to understand why the pendulum might only rotate 80% or so depending on how far north it was. (Easy to derive mathematically, but hard to truly intuit what was going on.)
As I doubt I'm the only one, allow me to provide the thought expirement that make it click for me; specifically, why the pendulum turns some fraction of a complete rotation while the Earth -- at any point -- makes a full circuit every 24 hours.
Put a pendulum in your car. If you drive straight, the pendulum won't be affected. If you turn, of course, the pendulum will turn a bit. Easy to visualize so far. Now, let's stop the Earths rotation for a moment. Let's get in the car and with the Pendulum and drive due East from L.A. All the way to N. Carolina (or wherever due east would end up.) Across the Atlantic. Across Southern Europe, Asia, Pacific, and back to L.A.
Now I've been driving straight this entire time, so would the pendulum have moved?
Well, as it runs out, I HAVEN'T been driving 'straight'. The entire time, I would necessarily had to have been veering a little bit to the left to keep me in my due East path. If I was truly driving straight the entire time, I would have made a Great Circle and dipped down into Africa at some point.
In any case, as my desktop pendulum moves around the globe every 24 hours, it isn't traveling in a straight line... just as a car transporting it along its path would have to be curving a bit to stay on course.
This was the 'ah-ha' moment that allowed to understand the gradual increase in the pendulums rotation as you move north (or south) from the Great Circle of the equator.
Maybe that is common-sense for everyone else. If so, disregard. ;)