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.
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 at a little more than a degree north of the equator
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!
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.
I too have waited in vain for that silly peg to topple. 