Today’s Google image reminds us that Léon Foucault’s pendulum demonstrated the turning of the Earth. I understand that a pendulum suspended in the air and set in a straight swinging motion demonstrates that the surface under it rotates. But it is difficult for me to understand how this works at any other places on the earth other than the physical north and south axes of the globe. Aren’t all other points of the earth moving in a lateral direction?
Well, more lateral, yes. If you set one up at the equator, it won’t rotate; if you set one up at the pole it will rotate once per day. Anywhere in between will rotate, but slower than once per day. There’s one at the California Academy of Sciences that rotates 220 degrees per day, for instance. But it’s big enough that you can still see that slower rotation.
If I hang my pendulum directly over the earth’s axis then the ground below is rotating separately from the top pivot/swing point of the pendulum. (My understanding is that the swinging keeps the pendulum’s swing in the same plane in space at all times and the pivot allows the movement between it and the earth.) But anywhere else it seems like pivot/swing point is moving with the ground below it. So there would be no change between the bottom of the pendulum and the ground.
Consider this: If you had a pendulum that was five feet away from the exact point of the North Pole, what would you expect it to do? You’d expect it to be almost indistinguishable from the one right exactly on the Pole, right? Now put another pendulum five feet away from that one, and another, and so on. The behavior of the pendulum must change gradually as the latitude changes.
I don’t have much to add besides the fact that you are not alone. I also struggle to visualize the full movement in my head.
On a globe in my head I can imagine the Foucault pendulum and its movements on the North Pole and I can imagine one on the equator. I know these are the two extremes and they makes sense to me. The in-between latitudes must have in-between behaviors, but the motions are too complicated for me to visualize.
The Indiana State Museum has (or had) one, suspended from the cupola in the center hall. It had a ring of candles on the floor, and the pendulum would knock one over ever 15 minutes. I’ve seen it, so I know it works, but don’t have any more explanation than the othes above.
This is cool! Thank you! I, like the others, have always wondered if there were some “skew” effect from the latitude. I’d never thought it through to realize that such a pendulum on the equator wouldn’t rotate, but, thinking on it now, sure! Of course it wouldn’t.
Is it described by a trig function, like the sine of the latitude? (Or cosine of the co-latitude?)
(Was gonna make a joke about toilets flushing, but never mind!)
The rotation rate/day is indeed the sine of the latitude. So at the poles, it’s once per day (the sign of the latitude indicating clockwise/counterclockwise turning). At the equator the rate is zero: no turning.
I was hoping that the rate of the Google doodle turning would be interesting. The latitude of Mountain View, CA. Or even better, the user’s latitude. But apparently not.
To the OP: Think of it this way. Start with the two point where the pendulum reaches it highest points at the ends of it swings. Imagine sighting along those two point out into space. That line doesn’t change. At the North pole, it’s aiming at something on the celestial equator. So as the ground turns underneath, it keeps aiming at the spot, appearing to turn.
At the equator, it’s aiming near Polaris. That point doesn’t change so no rotation. The sine function happens to nicely describe what happens in between.
What I want to know is, how does the pendulum keep swinging for that long? Shouldn’t air resistance shorten its swing over time?
You can change the Google doodle latitude.
They’re typically a very heavy weight at the end of a very long rod. Air resistance is pretty minimal, but yes, they do need to be “topped off” from time to time. Some installations have a small motor or actuator at the top. Others just have somebody give it a shove every few days.
magnets (scroll down to the last three paragraphs). There are probably other ways to do it as well.
There’s a big one at the Natural History Museum in San Diego. I grew up watching that thing…and I never noticed it rotated other than once per day! Just never paid that much attention! Duh!
When you watch it, you can hear the “click” of the electromagnets and relays (hey, it’s old!) that keep it moving. But, yeah, the weight at the end is also immense!
The Buffalo Museum of Science has one with big wooden bowling pin like pegs that are set up daily in a circle and get knocked down at regular times. I haven’t been there since I was a kid so can’t tell any details.
My school didn’t get to go there on field trips because years before some wise asses decided to hang off the edge of the stairwell and managed to stop the thing. Only school in the county declared Persona non grata. (that’s where I learned the term from), being told first day of 9th grade science class by a still bitter teacher.