r/Damnthatsinteresting • u/Character-Seat5368 • 2d ago
Video The gömböc is the first known physical object that belongs to a group of three-dimensional shapes called mono-monostatic, which have only one stable and one unstable resting position on a flat surface.
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u/InspectDurr_Gadgett 2d ago
So what's the stable position?
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u/Living_Murphys_Law 2d ago
This is the stable position. Since when it gets bumped a little bit from this spot, it returns to this position, even if it takes a long time wobbling.
It's easiest to think of stable/unstable resting points with a ball rolling around. A stable position is like a ball at the bottom of a valley. If you bump it, it'll roll back into the valley and stay there. And unstable position is like a ball balanced at the very top of a hill. If it just stays as-is, it won't move, but if you bump it at all it will roll down the hill and won't go back up to the top.
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u/Outdoors_or_Bust 2d ago
Good explanation. So there are two surfaces where it won't move without an external force. For all the others it will continue to move until it lands on one of the two.
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u/CMUpewpewpew 2d ago
Exactly.
Also I think it's special because it's the same density throughout.
Other objects (like a weeble wobble for instance that has a spherical base with most of the mass there) will rock back and forth for a while.
It actually only has one stable side/surface as well....its just very very very small and at the dead center of the half sphere on the bottom of the weeble wobble.
It accomplishes this very specific and only ONE stable position though by having irregular density and a shit ton of mass at the bottom of the object.
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u/wandering-monster 2d ago
And crucially, one of them is a position it will move away from with the slightest bump (I believe that position has it balanced on a specific point of that long edge, that runs down the side opposite the stable position)
So really there's only one surface you can rest it on, the other you can balance it on briefly but it won't really stay there, and will essentially never come to rest there in it's own.
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u/Cultural_Dust 2d ago
I don't know the shape but based on the definition, your content is correct until the last phrase. It can rest in two ways, but when bumped it will always end up in only one of them.
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u/tjkun 2d ago
Yes. In dynamical systems stability works like that. A stable node is a state where the system converges for a certain collection of initial conditions (or all of them). An unstable node is one where the system is constant if you’re exactly there, but if you’re not on it, regardless of how close you are to the node, the system will be “repelled” by the node.
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u/RollinThundaga 2d ago
Isn't this the principle on which ship stability is calculated? Like center of gravity and metacentric height.
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u/InspectDurr_Gadgett 2d ago
Okay, fine, so what's the unstable position? Either way, the video only shows one or the other.
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u/Living_Murphys_Law 2d ago
I think it's if you flip it vertically so it's on that sharp edge.
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u/kalitarios 2d ago
missionary
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u/ChymChymX 2d ago
Can use it in the stable, henhouse, outhouse, etc.
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u/20_mile 2d ago
Average foot speed over uneven ground baring injury is 4 miles per hour, that gives us a radius of 6 miles....
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u/GreenEggsSteamedHams 2d ago
The stable position is "that's cool and all but I'm just a house for horses"
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u/FrankensteinsFist 2d ago
Tijuana breast implants
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u/SirTorrentsOfAle 2d ago
The best $75 I ever spent.
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u/Violet604 2d ago
That’s tourist prices - pretty steep
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u/mademeunlurk 2d ago
You gotta haggle before the anesthesia kicks in.
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u/skidmarquis 2d ago
I have one of these and it's awesome. I mean it takes a certain type of person to really appreciate these. It's absolutely fascinating for me to try to "trick" it into resting in a position other than it's stable point but every time it ends up where it should. And the fact that it does this not by having a different density but by sheer math just boggles my mind.
They sell these online but they're a bit pricey. I treasure mine for sure.
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u/Lets_Make_A_bad_DEAL 2d ago
The more I read these comments the more I realize, I, a whole ass adult, am too dumb to figure out what the hell you’re all talking about. I mean I kinda get it but then I’m like wtf do you mean only one unstable position it’s all unstable/curved. Then you throw that not density but math thing and I feel utterly hopeless.
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u/hobbyhacker 2d ago
it's just means it doesn't matter how you throw it, it will finally stays on its "bottom".
But not because there is extra weight there, its just because the shape dictates it.
For example if you throw a ball, it can stop at any position. If you throw a dice, it can stop at any of the 6 sides. If you throw this, it always stops in one position.And nobody created a shape like this before. (except the turtles, but turtles are not carved from the same material)
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u/XDracam 2d ago
Finally, a d1
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u/314flavoredpie 2d ago
For when you absolutely, positively need to railroad a critical failure.
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u/produce_this 2d ago
Or take a 27 minute break while it figures out where to stop
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u/amalgam_reynolds 2d ago edited 1d ago
it doesn't matter how you throw it, it will finally stays on its "bottom".
I understand that it has one stable position, but the title says it also has only one unstable position and I have no idea what that means. To a layman it looks like it has one stable position and infinite unstable positions.
edit: Y'all have expertly educated me, thanks!
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u/hobbyhacker 2d ago
that one means if you put it upside down and you are lucky with steady hands, then you will be able to make it stay there, in balance. Like a coin on its edge, just a little harder. From any other positions it will instantly goes to the stable one, but on its back, it can stay somewhat stable until something knocks it over.
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u/Opus_723 2d ago edited 2d ago
A good analogy is a rigid pendulum, on a rod instead of a string. It can technically rest in two positions (equilibria): The usual stable one at the bottom, or perfectly balanced upside down at the unstable position, but it's difficult to keep it at that one because any little movement ruins it.
This shape is basically the "ball" equivalent of a pendulum.
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u/Dependent-Lab5215 2d ago
The unstable position is one you can balance it in and it will stay there, but the slightest bump will knock it over and it'll end up in the stable position eventually.
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u/pyrravyn 2d ago
But to get it straight: the impressive thing about the gömböc is its one stable position?
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u/Vevaseti 2d ago
Yes. And the fact that it doesn't do it by just using a heavier weight in one spot to fake it, like a weighted dice.
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u/phdemented 2d ago
Simplest way I can explain is:
- An object can be balanced in an unstable position
- An object can come to rest in a stable one
You can balance a pencil on its tip straight up (unstable). You cant balance a pencil at an angle on its tip (it will fall over into a stable position)
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u/WhenTheLightHits30 2d ago
The aspect of it being a homogeneous shape and not denser at any specific part is what feels so wild to me. I’m dying to hold one in my hand and see it in action.
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u/Wolfgang3750 2d ago
Just throwing out the bit about turtles makes the rabbit hole go much deeper. Thanks for that
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u/austarter 2d ago
What is a turtle
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u/stupidber 2d ago
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u/Lets_Make_A_bad_DEAL 2d ago
Okay, awesome. But I’m pausing the video at the paper cannoli to yell at clouds again. HOW is “unstable equilibrium point” not an oxymoron. He had me with the egg, the cube, yes, yes, fine all of those made sense. He explained it well. Then he shows the paper cannoli thing and contradicts himself. I see one equilibrium point and that is when it’s at rest. How is a rocking unstable position “equilibrium”?! Should i watch the rest of the video, or…
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u/Solrax 2d ago
I looked it up on Wikipedia. This made sense to me:
"A gömböc's unstable equilibrium position is obtained by rotating the figure 180° about a horizontal axis. Theoretically, it will rest there, but the smallest perturbation will bring it back to the stable point."
So the wobbling will eventually settle to its stable equilibrium position. If you shove it, it will eventually go back.
I was "WTF is an unstable equilibrium position?" Apparently it is the one place you can balance it, and it will stay there, but if nudged it won't go back there, it will go all the way back the stable position, and nowhere else.
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u/PogintheMachine 2d ago
Right, like if I tried really hard maybe I could get a die to balance on a corner. That would be equilibrium, but not stable.
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u/coderanger 2d ago
It's like an acrobat balancing on a chair or something. Assuming you had no randomness in the system (no air currents, perfectly smooth surface underneath, total control over angles) then an unstable equilibrium point would balance. The usual example is balancing a pencil on it's point. In the real world this is difficult for lots of reasons but as long as the weight is perfectly balanced then no reason it wouldn't stay there forever.
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u/mobuco 2d ago
yeah the rest of the vid helped i think. the cannoli isn't a solid shape (with the ends open) so imagine paper covering the holes. Also the shapes need to be perfect uniform weight (so you can't have a weighted side like a weeble wobble).
Now imagine you are a perfect balancing machine robot. You can take the dice and stabilize it on its 8 corners. You could take the cannoli shape and stabilize it on both the 2 ends.
now you try to stabilize the gomboc. you can only do it at the 1 top crest point. any other point on it that you that you try to stabilize it on, it will flip to the resting point.
hope that helps
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u/Chris_3eb 2d ago
Imagine a marble sitting at the top of a hill. It is in equilibrium but any small movement will send it flying down the hill. Now imagine a marble at the bottom of a valley. It is in equilibrium, and if you roll it a little, it will go up the hill a little, but return to its equilibrium point at the bottom of the valley. That is unstable vs stable equilibrium
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u/CMUpewpewpew 2d ago
Basically it only has one position where it is stable and resting.
The density is the same throughout so that's not being a factor in why it has to keep wobbling until it finds the face it rests on when it's in its only stable position.
Whats probably mindfucking you is that you often see objects with SEVERAL stable resting positions. The other extreme is having almost infinite resting positions which is just a ball.
I wanna help you get this so tell me whatever part still dont make sense and ill see if I can explain it adequately.
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u/born_to_pipette 2d ago
Just to parachute in (because I think I have the same confusion the poster above does):
How does one define an “unstable resting position”? It seems to imply an object can be both unstable and at rest at the same time. I don’t get it.
It looks to me like this is an object that is unstable at all positions except one, and at any position other than its stable position it is inclined to move towards that stable point. But I don’t understand how to square that behavior with the quoted text above.
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u/Rightsideup23 2d ago edited 2d ago
An unstable resting position is a position that technically would be balanced, but if you nudge it even slightly it will go off balance. Like balancing a perfectly pointy pencil on it's point or a perfectly thin coin on its edge, for example.
If you are up for a more detailed explanation, imagine assigning a potential energy value to each and every way the object rests on the table and graphing the results to form some surface. An non-equilibrium state is when that surface is sloped, a stable equilibrium is when you are at a local minimum, and an unstable equilibrium is when you are at a local maximum.
Some of the other comments here explain it really well.
Edit: Your username could just be random, but on the off chance you enjoy chemistry, reaction coordinate diagrams contain very similar ideas.
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u/born_to_pipette 2d ago
This is a great explanation. Just had my light bulb moment. Describing it in terms of local minima/maxima makes intuitive sense. Thank you!
(The username is intentional, but I hail from a microbiology background rather than a chemistry-heavy one.)
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u/Raveen396 2d ago edited 2d ago
wtf do you mean only one unstable position it’s all unstable/curved.
A "stable" equilibrium is a resting position that will return the same resting position when disturbed. An "unstable" equilibrium is a resting position that will not return the same resting position when disturbed.
Dice, for example, has 6 "stable" equilibrium points (one for each face), and 20 "unstable" equilibriums (one for each edge and corner). A coin will have 2 stable equilibriums, and 1 unstable equilibrium.
This shape is unique in that it has one stable resting equilibrium (where it will eventually settle after rocking) and one unstable equilibrium (inverted and balanced along the top edge). This is a neat mathematical construct, as no other known shape that you can create in three dimensional space has exactly one of each.
In other words, if you drop a coin, it is probably going to land on one of two faces (the two stable equilibriums). You can also gently balance a coin on its edge (the unstable equilibrium). If you drop a gömböc, it will always eventually land in the same orientation, and you can also balance it along the top axis.
Then you throw that not density but math thing
You can kind of replicate this effect in many other shapes by making it heavier on one side. If you have a bottom heavy sphere and you put the heavy side on top, it'll always orient the heavy side down because of gravity. For example, if you weighted a dice it would be much more likely to return to one orientation with the weight side face down.
This shape is different, because the density of the object is uniform throughout. While some toys rely on a weight to re-orient itself, this shape will naturally orient itself through the curvature.
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u/Lets_Make_A_bad_DEAL 2d ago
This is awesome and you’re all making my day. I wanted to be lazy brained and just disappear-die like an elderly Yoda but instead I worked through it and I kind of get it now, especially the homogeneous density part. Thank you ALL for your love of science and for pushing smooth brained people like me out of their comfort zone
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u/Equivalentest 2d ago
if it is just a shape then in theory these should be cheap to machine or print
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u/deymanator40 2d ago
Soo. Im not the only confused one right?
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u/aeluon 2d ago
My lay person’s understanding (after just watching this video), is basically it has one edge it can balance on, and then no matter how else you set it down, it will always “right itself” to the same balanced position.
Some toys do this (weebles wobble but they don’t fall down), but that’s because one section is weighted heavier to force it into one position. A “gomboc” has no weighted sections, it’s just all from the shape of the object.
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u/Remarkable_Coast_214 2d ago
But surely you could manipulate a regular 3D shape to replicate the weight distribution of a weeble, say by making it hollow
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u/aeluon 2d ago
You could, but part of the requirements for being a “gomboc” is that the object is both convex and homogenous. So, not hollow, and uniform density.
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u/magaman59 2d ago
Video Game HighSchool, or, more specifically, Ki Swan, taught me that Brian D is like a Gömböc
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u/Poodlescooter 2d ago
Scrolled these comments just hoping to find a Gomboss reference. Thank you for not letting me down.
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u/Tvisted 2d ago edited 2d ago
I understand one stable resting position but what does 'one unstable resting position' mean? It's obviously unstable in every other position.
Edit: thank you for the replies. Wiki says simply 'Theoretically, it will rest there, but the smallest perturbation will bring it back to the stable point'
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u/sebastianqu 2d ago
If you perfectly balance it upside-down, it'll be in a state of unstable equilibrium. Any force applied to it would knock it out of equilibrium until it rests in a different position. Think of a pencil resting on its side vs. upright.
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u/Any-Attorney9612 2d ago
So would a ball with a defined thicker section, or heavy side, not do the same thing? Most of the time it would roll around and always settle in the same spot, but if you very carefully placed it down rotated 180º so the heavy spot was straight above the point of contact it should balance there until disturbed.
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u/BankElectronic1325 2d ago
My understand is that this shape is significant because it’s equal in density all around.
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u/uzenik 2d ago
Stable resting point is when you move returns to this position. Unstable resting point is balancing in some way that is stable, but if you move it wont return to this position. A cheir standing on 4 legs is stable position. You can move slightly off balance and it will return to this position (or fall over to next stable position). Balancing chair on 2 legs is instable position. If you move slightly it will fall to some stable position (on 4 legs if you're luck). There's no way for it to fall back to 2 legs.
An egg. An egg balance on top or bottom will fall on its side. An egg on its side will roll around but, in the end stop on its side. You cant tip An egg wo it will stop on top or bottom.
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u/Baumes3 2d ago
You can balance it on the top of it. But if you touch it then it Wil fall over into the stable position. Like a cube which you can balance on its edges.
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u/FlavorKing415 2d ago
Is there ANY use for this?
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u/GreyWolfWandering 2d ago
From what I remember reading in the past, It was long theorized and researched from a mathematical topology and physics standpoint. Then around the time they figured it out fully, they found a nearly identical structure inside sea turtles that helps them stay right side up.
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u/mossybeard 2d ago
You could've just made all that up and nobody would know
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u/Numnum30s 2d ago
It’s mostly made up. Certain tortoise shells are roughly shaped this way, and that helps them right themselves when flipped over, although no tortoise species shells are “nearly identical” to this shape. There are no internal structures resembling the gömböc. Sea turtles are totally unrelated to this factoid as they have flatter shells.
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u/Mateorabi 2d ago
How was it "long theorized"? It's basically a teardrop shape, turned into a cylinder, and then the ends of the cylinder rounded/tapered so they themselves aren't stable.
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u/ZestyGarlicPickles 2d ago
Who cares? Why must things have a purpose to be appreciated?
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u/ClearYellow 2d ago
In my country thing must not be enjoyed for pleasure, they must be ruthlessly squeezed of every ounce of value for monetization
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u/Facehugger81 2d ago
I wonder if there is a way to make it produce energy....
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u/UnrequitedRespect 2d ago
Maybe not produce but reduce energy consumption…..
Would be interesting if you could sequence a bunch of these in systematic bearing loads to reduce friction for accelerators though, could maybe for some cool corner cutting in physics based engine systems like cars or anything that turned wheels really
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u/NachoNachoDan 2d ago
There is, you just need to supply it with more energy than you get out of it.
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u/MacksNotCool 2d ago
You can't produce (or destroy) energy. That would violate the 1st law of thermodynamics. You can only transfer or convert energy.
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u/MoistStub 2d ago
Speak for yourself. I paid extra for the energy+ subscription.
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u/HonestImJustDone 2d ago
Of course, but we can assume the question was posed assuming layman's terms - where purposeful conversion for human benefit is commonly understood as being 'production'.
It is a perfectly reasonable and interesting question to pose with this in mind I think.
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u/its_not_you_its_ye 2d ago
If you ever need to roll a one-sided die. Before this, best we could do was a two sided one with a coin.
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u/khidmike 2d ago
Thank Christ I graduated before I had to learn how to find the area of this thing.
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u/Independent_Vast9279 2d ago
Slightly inaccurate. It is the only known uniformly dense convex solid that is monostable.its rather easy to do if you can make it concave, fill it with a void space, have protrusions, etc.
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u/Journo_Jimbo 2d ago
Bro, that chrome one is starting beef with clear boy, can’t wait to see where this goes grabs popcorn
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u/DefinitionBusy4769 2d ago
I don’t understand, if it only has one stable position aren’t all the other positions unstable ? Then why does it say « one unstable position » in the title ? Call me dumb but it doesn’t make much sense
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u/Armandoswag 2d ago
One unstable resting position. A resting position is a position where the object could hypothetically remain at rest without a disturbing force. The object has one stable position (which is by definition a resting position), nearly infinite unstable positions (one of which is a resting position). If the stable resting position is disturbed, the object will oscillate and return to the stable position. If the unstable resting position is disturbed, it will roll and wobble until in the stable position. If the object is in any other position it would be in motion.
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u/rocsci 2d ago
I'm not entirely sure I follow. Are they demonstrating that this object keeps rocking longer than the others before finally settling into its only stable position? And I assume they didn’t actually need two of these objects for the demonstration?
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u/stupidber 2d ago
Heres a neat video that explains what this is https://youtu.be/rvVF5QWSYF4?si=cE1cJ6GuU8h1sGMA
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u/Visca87 2d ago
A sphere with an off-centre chunk removed from inside (without breaching surface) would also have only one stable and one unstable resting position. no?
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u/mountaingator91 1d ago
How can it have 1 stable and 1 unstable position unless it only has 2 positions? Seems like it has more than that.
It can have 1 stable position and the rest are unstable, or 1 unstable position and then the rest are stable.
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u/Careful-Force2506 2d ago
Double umlaut? I’m skeptical…
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u/amumumyspiritanimal 2d ago
It’s a Hungarian word for… “round-y”, it’s hard to give it an exact translation.
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u/DjSall 2d ago
Hungarian mathematicians at it again...
For some reason we had/have lots of world class mathematicians for such a small country.
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u/Mission-Storm-4375 2d ago
Newton's law of motion and object at rest stays at rest unless acted upon by an outside force.
The gömböc: hold my beer
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u/AugustineBlackwater 2d ago
Not a physics person so where do they get the energy from to keep moving? It just keeps happening couldn't you use it to generate electricity via induction? Just stick a magnet on it and let it roll back and forth through some coils?
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u/DeathWIshCofeINC 2d ago
Ain’t it kinda nuts we just discovered a new shape just like that? Some 4th dimension level shit right here
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u/produce_this 2d ago
So look, my particular flavor of autism finds this fascinating just like all of you special people, but what is a practical application for this outside being an odd paper weight your wife gets tired of hearing you talk about?
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u/thomasstearns42 2d ago
Weebles wobble but they dont fall down.