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Foucault pendulum

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Re: Foucault pendulum

#11

Post by lurquer »

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. ;)

Re: Foucault pendulum

#12

Post by aidenn0 »

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.

Re: Foucault pendulum

#13

Post by fatnoah »

lurquer wrote: post #11

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 s…

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.

Re: Foucault pendulum

#17

Post by lurquer »

fatnoah wrote: post #13
lurquer wrote: post #11

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 s…

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.

Re: Foucault pendulum

#18

Post by rubatuga »

frenchie4111 wrote: post #15

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.

Re: Foucault pendulum

#19

Post by Ididntdothis »

lurquer wrote: post #11

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 s…

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.

Re: Foucault pendulum

#20

Post by leni536 »

lurquer wrote: post #11

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 s…

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?

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