# Foucault's Pendulum **URL:** \ **Category:** Factual Questions\ **Created:** [April 14, 2003, 6:06pm UTC](https://boards.straightdope.com/t/foucaults-pendulum/168690 "2003-04-14T18:06:36Z")\ **Posts on this page:** 9\ **Page:** 1
**Author:** ![Greg\_Charles](https://avatars.discourse-cdn.com/v4/letter/g/839c29/32.png) [@Greg\_Charles](https://boards.straightdope.com/u/Greg_Charles)\ **Post date:** [April 14, 2003, 6:06pm UTC](https://boards.straightdope.com/t/foucaults-pendulum/168690/1 "2003-04-14T18:06:36Z")
Yesterday, I spent entirely too much time watching one of those Foucault’s pendulums as it made torturously slow progress towards knocking down a wooden peg. (A Foucault’s pendulum consists of a large metal ball swing at the end of a long cable. As the earth rotates underneath it, the plane of the ball’s swing seems to rotate slowly relative to the floor, and any wooden pegs that happen to be set there.) During my wait (some might say obsessive wait), I read the sign and found out that the pendulum wouldn’t do a full rotation in a day, as I had assumed, but would take about 44.5 hours. The nominal explanation for this had something to do with our latitude and imagining ourselves on a wobbly barrel. Somehow, that didn’t fully sink in, possibly because I had to interrupt my thinking every two-and-a-half seconds to make sure I didn’t miss the swing that would finally knock over that damned wooden peg! I’m hoping someone in the Teeming M. can provide a more lucid explanation of the phenomenon. An equation relating latitude to rotation time would also be cool. P.S. The museum closed and I was kicked out with that blasted wooden peg still standing. I swear I heard it laughing at me as I shuffled towards the door. ---
**Author:** ![CalMeacham](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/calmeacham/32/35_2.png) [@CalMeacham](https://boards.straightdope.com/u/CalMeacham)\ **Post date:** [April 14, 2003, 6:25pm UTC](https://boards.straightdope.com/t/foucaults-pendulum/168690/2 "2003-04-14T18:25:11Z")
There’s an explanation of it in Kleppner and Kolenkow’s **Introduction to Mechanics** – great rigorous-math-based physics course! ---
**Author:** ![Encinitas](https://avatars.discourse-cdn.com/v4/letter/e/ee7513/32.png) [@Encinitas](https://boards.straightdope.com/u/Encinitas)\ **Post date:** [April 14, 2003, 7:01pm UTC](https://boards.straightdope.com/t/foucaults-pendulum/168690/3 "2003-04-14T19:01:09Z")
Went to the Natural History Museum in Balboa Park didn’t ya **Greg Charles**. 🙂 I too have waited in vain for that silly peg to topple. ☹ ---
**Author:** ![Skammer](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/skammer/32/143_2.png) [@Skammer](https://boards.straightdope.com/u/Skammer)\ **Post date:** [April 14, 2003, 7:12pm UTC](https://boards.straightdope.com/t/foucaults-pendulum/168690/4 "2003-04-14T19:12:36Z")
Is it somebody’s job to climb into the display and reset the pegs every morning? ---
**Author:** ![chukhung](https://avatars.discourse-cdn.com/v4/letter/c/e79b87/32.png) [@chukhung](https://boards.straightdope.com/u/chukhung)\ **Post date:** [April 14, 2003, 7:20pm UTC](https://boards.straightdope.com/t/foucaults-pendulum/168690/5 "2003-04-14T19:20:51Z")
This site, [http://www.phys.unsw.edu.au/PHYSICS\_!/FOUCAULT\_PENDULUM/foucault\_pendulum.html](http://www.phys.unsw.edu.au/PHYSICS_!/FOUCAULT_PENDULUM/foucault_pendulum.html) has a fairly cogent explanation of the phenomenon. > [@](#): > > Suppose someone put a pendulum above the South Pole and sets it swinging in a simple arc. To someone directly above the Pole and not turning with the earth, the pendulum would seem to trace repeatedly an arc in the same plane while the earth rotated slowly clockwise below it. To someone on the earth, however, the earth seems to be stationary, and the plane of the pendulum’s motion would seem to move slowly anticlockwise, viewed from above. We say that the pendulum’s motion precesses. The earth turns on its axis every 23.93 hours, so to the terrestrial observer at the pole, the plane of the pendulum seems to precess through 360 degrees in that time. > > The situation is more complicated for other latitudes. On the equator, the pendulum would not precess at all - its precession period is infinite. At intermediate latitudes the period has intermediate values. The link at the bottom of page has all the hairy mathematics. I always wondered what the lowest latitude for a museum display of a Foucalt pendulum is. Imagine how long you’d have to wait for that peg to fall at the [Singapore Science Centre](http://www.science.edu.sg/ssc/index.jsp) at a little more than a degree north of the equator ---
**Author:** ![Trinopus](https://avatars.discourse-cdn.com/v4/letter/t/2bfe46/32.png) [@Trinopus](https://boards.straightdope.com/u/Trinopus)\ **Post date:** [April 14, 2003, 8:01pm UTC](https://boards.straightdope.com/t/foucaults-pendulum/168690/6 "2003-04-14T20:01:03Z")
> [@](#): > > \*Originally posted by Encinitas \* > \*\*Went to the Natural History Museum in Balboa Park didn’t ya **Greg Charles**. 🙂 I too have waited in vain for that silly peg to topple. ☹ \*\* Me too, neighbor: me too! **Skammer** : Yes. Trinopus ---
**Author:** ![Greg\_Charles](https://avatars.discourse-cdn.com/v4/letter/g/839c29/32.png) [@Greg\_Charles](https://boards.straightdope.com/u/Greg_Charles)\ **Post date:** [April 14, 2003, 8:39pm UTC](https://boards.straightdope.com/t/foucaults-pendulum/168690/7 "2003-04-14T20:39:06Z")
Yes, **Encinitas** , the Natural History Museum was where this particular Foucault’s pendulum was swinging. In answer **Skammer** ’s question, the woman who kicked me out also stopped the pendulum, although at my request, and with the air of one who is humoring a madman, she did knock over the peg for me. I imagine it is also her job set up the pegs in the morning and re-swing the pendulum. Actually, I suspect she just sets out a line of “knocked over” pegs and one standing one. It will take me awhile to digest the math in **chukhung** ’s link. The final analysis though is the rotation period is 23.93 hours divided by the sine of the latitude. That does work out to 44.5 hours for San Diego. It sort of begs the question, though, why 23.93 hours? I was pretty sure that the earth rotated on its axis every 24 hours. Are we really losing 4.7 minutes per day? No wonder I’m always behind! ---
**Author:** ![William\_Ashbless](https://avatars.discourse-cdn.com/v4/letter/w/a87d85/32.png) [@William\_Ashbless](https://boards.straightdope.com/u/William_Ashbless)\ **Post date:** [April 14, 2003, 8:48pm UTC](https://boards.straightdope.com/t/foucaults-pendulum/168690/8 "2003-04-14T20:48:00Z")
I suspect it has something to do with the fact that Earth is moving happily along its orbit around the sun. 24 hours would be the time it takes the Sun to return to the its highest point overhead, but to do this as Earth goes around the sun the Earth has to over-rotate slightly. (This is easier to see if you consider that in a quarter year the Earth has moved 90 degrees around in its orbit of the sun approximately, so compared to now the Earth will have to rotate an extra 90 degrees over the course of a quarter year to have the sun appear ‘overhead’). So the time it takes to rotate around 360 degrees is actually less than 24 hours. The 24 hours is to rotate around 360 degrees plus… well, 360 degrees extra over an entire year, so almost an extra degree per day. Just a guess. ---
**Author:** ![chukhung](https://avatars.discourse-cdn.com/v4/letter/c/e79b87/32.png) [@chukhung](https://boards.straightdope.com/u/chukhung)\ **Post date:** [April 14, 2003, 8:51pm UTC](https://boards.straightdope.com/t/foucaults-pendulum/168690/9 "2003-04-14T20:51:41Z")
> [@](#): > > \*Originally posted by Greg Charles \* > \*\*I was pretty sure that the earth rotated on its axis every 24 hours. Are we really losing 4.7 minutes per day? No wonder I’m always behind! \*\* Keep in mind that not only is the earth rotating on it’s axis, it’s also revolving around the sun. There’s an explanation (and a nifty little diagram) of this phenomenon on this page, [http://www.phys.uconn.edu/~mcdonald/ph155/sidereal.html](http://www.phys.uconn.edu/~mcdonald/ph155/sidereal.html) > [@](#): > > Careful observation of the sky will show that any specific star will cross directly overhead (on the meridian) about four minutes earlier every day. In other words, the day according to the stars (the sidereal day) is about four minutes shorter than the day according to the sun (the solar day). > > If we measure a day from noon to noon - from when the sun crosses the meridian (directly overhead) to when the sun crosses the meridian again - we will find the average solar day is about 24 hours. If we measure the day according to a particular star - from when that star crosses the meridian to when that star crosses the meridian again - we will find the average sidereal day is 23 hours and 56 minutes.