If you run a pendulum at the equator for a year, will it turn a circle?
That’s an excellent link …I will study it closely.
Yes, but you need to think of that as a blend of the two cases of swinging exactly perpendicular to the equator, and swinging exactly in line with the equator - both of which result in a straight swing, therefore the blended case should too.
Agreed. I wrote half a post about imagining the roundabout as a hemisphere, not a disk, and having magical magnetic shoes so you could stand anywhere on the surface, but abandoned it as too confusing.
A perhaps useful* analogue to the equator case is the wall of death fairground ride. Were it not for the overwhelming centrifugal forces, occupants of the ride could move up and down in place without deflection of course (because their heads and feet are in the same reference frame) and could move around the diameter of the thing, because that only amounts to going faster or slower in the direction already travelled.
*Perhaps not though, because the forces generated by the rotation are difficult to ignore.
Nope, zero rotation is zero rotation.
Imagine you started one at the equator lined up perfectly in parallel with it. It would continue oscillating east-west as the Earth turns and moves around the Sun.
It’s just easier to see for that angle, but all others at the equator are equivalent.
OTOH, the precession of the Earth’s tilt would have an effect. A small wobble over 26000 years.
Oh,yeah, I see. The earth itself is a big gyroscope, also holding a fixed orientation to the stars (except for precession).
Yeah, mine too!
The reason the line isn’t centered is because the fulcrum moves. Yes, it stays in the same plane (which is why the pendulum stays in a plane, thus “exscribing” a line). But it advances in a curve the direction of the Earth’s rotation, which means, the situation is asymmetric about the (nonlinearly moving) fulcrum. How that exactly plays out I’m not sure, I just doubt the result to be symmetric. If the fulcrum were moving linearly, I’d expect it to be symmetric, but I’m not even sure about that, and it’s just not possible unless the Earth (the body producing the gravitation) has infinite radius, or isn’t spherical, or something.
I think that’s easier. The playground roundabout is a good analogy. I always imagined a bug on a spinning record, which amounts to the same thing, and also provides nearly cylindrical lines of reference (the grooves).
If the bug takes a step towards the spindle, his previous velocity in the direction of rotation is now higher than everything else at his new radius. For that reason, he tends to slide in the direction of rotation. Since a record turns clockwise, that means he slides left a bit, before coming to equilibrium with his new location.
If he takes a step away from the spindle, his previous velocity in the direction of rotation is now lower than everything else at his new radius, so slides a bit opposite the direction of rotation. Again, this is to the left.
If he takes a step in the direction of rotation, he’s now going faster than everything at his radius. That makes him experience even more centrifugal force, which tends to make him slide outward (even more than the normal case, when he’s sitting still). So, again, he slides to the left.
The opposite direction is left to the reader as an exercise. 
In 3D it’s a bit more complicated but really quite the same thing going on, and even the apparent direction of the coriolis force is the same. But I’ve buggered something up here, because in the Northern hemisphere, the coriolis force turns us to the left, IIRC, yet we’re spinning counterclockwise when viewed from above the North pole. Hrmph.
I’ve often imagined ball sports in a huge room in a rotating space station, and how it would affect things like passing. Here you get coriolis effect, but in 3D. Imagine ping-pong, where the table is aligned with the direction of rotation! One player would tend to hit floaters and the other would have wicked faux-topspin. Imagine a football field aligned to the rotation. Lateral passes would curve wickedly. It’d be fun to get a chance to play enough to understand the paths intuitively!
Most likely, though, I’d barf. Despite being an avid sailor, I’m a bit prone to seasickness. I remember waking in the early morning during an overnight sailing race in strong winds, where the boat was heeling 30-45 degrees. On awaking, without thinking I braced myself against the heeling as I moved. Yet, when I went to fill my cup with water, I instinctively put the cup between the faucet and the drain. I turned the water on, and it flowed in a sharp angle from the faucet to the corner of the sink, completely missing my cup! :eek:
I had to make a bee line topside, to the low side.
oops
The Smithsonian used to (maybe still does) have an enormous pendulum (something like 20’ diameter swing) that would knock down little posts arrayed in a circle every 15 minutes. It was always one of my favorite exhibits.
I bet that’s it. My recollection is very hazy and possibly augmented with what I’ve since learned about Lissajous figures, etc. I would have seen the one at the Smithsonian in 1967 at age 10. I’ve been there since, but not to that particular exhibit. I need to go back to DC soon!
The Boston Museum of Science has one, too. It’s suspended over a mosaic replica of the Aztec Calendar Stone, and they set up a line of metal pegs (on metal bases) at the start of each day to have them knocked over.
The FRanklin Institute in Philadelphia has one, as well, although I don’t recall the pegs with theirs.
A Foucault pendulum isn’t hard to set up. My high school physics teacher set one up using a ten pound weight, a length of cable, and a Universal Joint. He suspended it from the ceiling and started it along one of the joints in the tile floor by holding it along the joint and having a student put a match to the thread holding it off-center. This was at the start of a test we were taking during the period. By the time the test was over, you could clearly see that the plane of rotation had tilted.
There’s also a large one at the natural history museum in San Diego: The Nat |
Also Chicago Museum of Science & Industry
I share the Poster’s confusion. This has always bothered me, too! And, I think the crux of the confusion we need someone to explain this, bit by bit:
The videos do not help because, like every other explanation, all assume the point overhead from which the pendulum is hung is stationary*. Yet, when I look at a Foucault’s pendulum in the Smithsonian, I see a building, the pendulum, and the point overhead from which it is hung ALL AS ONE SYSTEM! These are ALL on the earth, all moving together with the earth’s rotation…whether the pendulum attaches direct to the ceiling, a well greased ball joint, or any other universal joint! They all rotate west to east together as one system! You cannot isolate and make stationary one component of this system from the next!
*Or, the point of rotation itself! But, you don’t simply set up a pendulum and the earth’s poles now magically rotate in line with your Focault’s pendulum!?!? (Very frustrating to understand! :eek:)
There is simply NO possible way it makes sense to say (as was always repeated to me) “the earth rotates beneath the pendulum moving the pins into the path of the pendulum”. Only if I built the Smithsonian at a pole could the earth rotate beneath it, and even then the building would have to be a point mass! The building will always rotate with the earth regardless of location! So, how can the pins appear to move into the path of the pendulum…or the pendulum appear to change course? (Personally, I see the pins moving into the path of the pendulum. Is this an optical illusion, like a relative motion effect?)
Aside: Even once this is clearly explained, wouldn’t a scientist really conclude there must be a force on the pendulum making this happen? At best, technically, one can conclude this is proof of the Coriolis Effect which we therefore assume is from the earth’s rotation.
Yes, the suspension point moves with the building, but the important part is that it allows free rotation.
Imagine hanging a pendulum from the centre of a wooden board, from a joint that allows free movement. Draw a line on the board and start the pendulum swinging below the board so that it aligns with the line. Now slowly rotate the board. Now walk around in a large circle while holding the board, with the pendulum swinging beneath it.
For an imaginary miniature observer attached to the underside of the board, looking down at the pendulum, what will the effect be?
I haven’t been able to find a diagram of the pendulum pivot - I’d love to know how this works.
The one at the Franklin Institute had a small-scale model showing the pendulum cable anchored in a sphere resting atop three other spheres. But you don’t need anything as complex as that. As I mentioned upthread, my high school physics teacher set up a Foucault pendulum in our classroom using an ordinary anchor point in the ceiling, with a universal joint shortly below it to allow the pendulum to swing freely in any direction.
The pivot assembly needs two things:
-
Something to prevent the slow rotation of the earth from imparting a twist to the pendulum support cable.
-
Something to power the pendulum’s swing against air drag & internal cable friction, also without imparting any twist to the pendulum’s motion. And without imparting any restorative force either; it’d be cheating to restrain the pendulum’s plane of motion.
The first half just needs to be a very low friction U-joint. A magnetic bearing would be another approach.
For the second half you need a fairly simple electric motor. A ring-shaped electromagnet some distance below the pivot can be pulsed to gently tug the cable uniformly outwards at the appropriate point in its swing. Since the whole system is high inertia & low friction, the tug doesn’t need to be very strong, nor very frequent.
Why do you need a motor? Those big pendulums in the museums have enough momentum to keep going on their own all day without an extra power source. And my high school physics example only had to run for an hour.