I found it very difficult to understand WHY Foucaults pendulum behaves the way it does.
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. ;)
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.
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.
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.
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]
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.
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.
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.
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.
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.
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.
lurquer|5 years ago
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. ;)
gregfjohnson|5 years ago
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.
leni536|5 years ago
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?
fatnoah|5 years ago
Ididntdothis|5 years ago
sandworm101|5 years ago
(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
erikig|5 years ago
[1] https://en.wikipedia.org/wiki/Cresson_Kearny
[2] https://en.wikipedia.org/wiki/Kearny_air_pump
mdturnerphys|5 years ago
spookybones|5 years ago
unknown|5 years ago
[deleted]
aidenn0|5 years ago
redis_mlc|5 years ago
https://www.youtube.com/watch?v=-p7P0DQvp0g
saagarjha|5 years ago
SlipperySlope|5 years ago
[deleted]
NegativeLatency|5 years ago
pengaru|5 years ago
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...
frenchie4111|5 years ago
rubatuga|5 years ago
lihaciudaniel|5 years ago
decasteve|5 years ago
empath75|5 years ago
The existence of the day-night cycle should have sufficed.
saagarjha|5 years ago
unknown|5 years ago
[deleted]
lidHanteyk|5 years ago
KMag|5 years ago
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.