Questions tagged [stability]

Stability theory addresses the stability of potentials, solutions of differential equations, and of trajectories of dynamical systems under small perturbations of initial conditions.

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Can we theoretically balance a perfectly symmetrical pencil on its one-atom tip?

I was asked by an undergrad student about this question. I think if we were to take away air molecules around the pencil and cool it to absolute zero, that pencil would theoretically balance. Am I ...
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64 votes
10 answers
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Why doesn't a bike/bicycle fall if going with a high speed?

Why does a bike/bicycle fall when its speed is very low or close to zero and is balanced when going with a high speed?
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50 votes
9 answers
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Why are $L_4$ and $L_5$ lagrangian points stable?

This diagram from wikipedia shows the gravitational potential energy of the sun-earth two body system, and demonstrates clearly the semi-stability of the $L_1$, $L_2$, and $L_3$ lagrangian points. The ...
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Why does this object periodically turn itself?

See below gif image taken from here. Or see this Youtube video about 30 sec in. Is this a real effect? Why does it seem to turn periodically? Can it be explained by classical mechanics alone? Is ...
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45 votes
4 answers
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Is it possible that every single isotope is radioactive, and isotopes which we call stable are actually unstable but have an extremely long half-life?

I've read that tellurium-128 has an half-life of $2.2 \times 10^{24}$ years, much bigger than the age of the universe. So I've thought that maybe every single isotope of every single atom are ...
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41 votes
4 answers
23k views

Why do most office chairs have 5 wheels?

(Inspired by Why are four legged chairs so common?) I've been wondering for a while... Why do most wheeled office chairs have 5 wheels? My guess would be that while stability vs. simplicity results ...
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37 votes
4 answers
39k views

Stability of rotation of a rectangular prism

I've noticed something curious about the rotation of a rectangular prism. If I take a box with height $\neq$ width $\neq$ depth and flip it into the air around different axes of rotation, some motions ...
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34 votes
7 answers
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How can the unstable particles of the standard model be considered particles in their own right if they immediately decay into stable particles?

How can the unstable particles of the standard model be considered particles in their own right if they immediately decay into stable particles? It would appear to a layman such as myself that these ...
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29 votes
10 answers
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Where did Schrödinger solve the radiating problem of Bohr's model?

One of the problems with Bohr's theory to describe the hydrogen atom, was that the electron orbiting around the nucleus has an acceleration. Therefore it radiates and loses energy, until it would ...
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27 votes
3 answers
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What does it mean when an isotope is stable?

Does stable mean that an isotope has a very long half life, for example xenon-124 has a half life of 1.8 x 10^22 years, or does it mean that fissure is theoretically not possible, or does it mean that ...
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25 votes
4 answers
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Gravity in other than 3 spatial dimensions and stable orbits

I have heard from here that stable orbits (ones that require a large amount of force to push it significantly out of it's elliptical path) can only exist in a three spatial dimensions because gravity ...
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23 votes
5 answers
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Why do unstable nuclei form?

Why do unstable nuclei form? Is it that we simply find unstable nuclei in nature and understand what these nuclei do in order to become more stable? I feel like textbooks gloss over this question ...
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3 answers
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Why certain rotations are unstable? (Euler Equations)

We have the Euler equations for a rotating body as follows $$I_1\dot\omega_1+\omega_2\omega_3(I_3-I_2)=0\\ I_2\dot\omega_2+\omega_1\omega_3(I_1-I_3)=0\\ I_3\dot\omega_3+\omega_2\omega_1(I_2-I_1)=0$$ ...
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23 votes
6 answers
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Why does the weighing balance restore when tilted and released

I'm talking about a Weighing Balance shown in the figure: Press & Hold on onside of the horizontal beam and then release it. It makes some oscillations and comes back to equilibrium like shown in ...
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22 votes
4 answers
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Confusion regarding the principle of least action in Landau & Lifshitz "The Classical Theory of Fields"

Edit: The previous title didn't really ask the same thing as the question (sorry about that), so I've changed it. To clarify, I understand that the action isn't always a minimum. My questions are in ...
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22 votes
3 answers
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Why is Larry Niven's Ringworld Unstable?

In his 1970 science fiction novel Ringworld, author Larry Niven describes the eponymous Ringworld, a gigantic structure shaped as a ring with a radius of around 1 AU, rotating around a star in the ...
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21 votes
4 answers
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Can there be an atomic nucleus where there are more protons than neutrons?

As far as I know, number of protons is less that or equal to the number of neutrons in any atomic nucleus. But is there any possibility that there exists a nucleus where the number of protons exceeds ...
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20 votes
4 answers
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Why are alpha particles such a prominent form of radiation and not other types of nucleon arrangement?

It is said in many textbooks that alpha decay involves emitting alpha particles, which are very stable. Indeed, the binding energy (~28.3 MeV) is higher than for $Z$-neighboring stable isotopes. But ...
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19 votes
10 answers
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Does leaning (banking) help cause turning on a bicycle?

I think it's clear enough that if you turn your bicycle's steering wheel left, while moving, and you don't lean left, the bike will fall over (to the right) as you turn. I figure this is because the ...
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18 votes
4 answers
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Staying in orbit - but doesn't any perturbation start a positive feedback?

I am not a physicist; I am a software engineer. While trying to fall asleep recently, I started thinking about the following. There are many explanations online of how any object stays in orbit. The ...
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18 votes
4 answers
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Why doesn't the deuterium nucleus have spin $0$?

A deuterium nucleus is composed of a proton and a neutron. Both have spin $\tfrac12$ so I would expect the deuterium to have two possible spins: $1$ for the triplet and $0$ for the singlet. But ...
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18 votes
2 answers
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Is there a quantum analogue of the "Tennis Racket" theorem?

A non-trivial result from studying the classical mechanics of an extended object shows that rotation about an axis whose moment of inertia is between the largest and smallest moment-of-inertia axes is ...
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18 votes
1 answer
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Does anyone know the mechanism behind this double helix cloud formation?

This looks like m=2 swirling instability mode of the axisymmetric jet, but how could an axisymmetric jet form up in the sky like that?
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16 votes
6 answers
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Why do we fall down when the bicycle slows down? [duplicate]

My question is: It is easy to balance a bicycle when it is moving at a fairly high velocity, say 7 m/s or 25 km/hr. But when a bicycle slows down, it is hard to keep it upright, and the person riding ...
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16 votes
3 answers
3k views

Why do all elements above $\require{mhchem}\ce{Fe}$ not decay to $\ce{Fe}$?

OK, so $\ce{Fe}$ is the most 'stable element'. As such, why do all elements above it not decay into $\ce{Fe}$? In all cases, would it not lead to an increase in binding energy and therefore energy ...
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16 votes
1 answer
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Why does a cuboid spin stably around two axes but not the third?

Let $C$ be a cuboid (rectangular parallelepiped) with edges of lengths $a < b < c$. Consider an axis that passes through the centers of two opposite faces of $C$. There are three such axes, ...
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15 votes
2 answers
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Conservative central force and stable orbits

I saw a question a few days ago which referred to Bertrand's theorem. So, I now know that stable, closed orbits only occur when the potential function is $\frac{-k}{r}$ or $\tfrac{1}{2}kr^2$. If ...
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15 votes
2 answers
568 views

Why are superfluid vortex lattices stable?

Both (a) neutral superfluids that are externally rotated, and (b) type-II superconductors (i.e. charged superfluids) under applied magnetic fields between the critical fields $h_{c1}$ and $h_{c2}$, ...
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15 votes
1 answer
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Why is the orbital resonance of the Galilean moons stable?

It is well known that the orbits of Ganymede, Europa and Io are in a 4:2:1 resonance. Most online sources (including but not limited to Wikipedia) say that such an orbital resonance, along with the 3:...
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15 votes
2 answers
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Bottle stability optimization

A few days ago some friends and I played a game called "flunkeyball" where you need to upset a bottle with a ball. Then a question occurred: "How much water do we need to put into the bottle that its ...
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14 votes
1 answer
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James Webb Space Telescope's halo orbit at Lagrange point L2

The James Webb Space Telescope (JWST) is expected to be launched in 2018 and operate in the L2 vicinity, about 1.5 million km from Earth. It will be placed in a halo orbit around the unstable L2 ...
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14 votes
1 answer
278 views

Theorems on instability of classical systems of charged particles?

Classically, a hydrogen atom should not be stable, since it should radiate away all its energy. I remember hearing from my favorite freshman physics prof ca. 1983 about a general theorem to the effect ...
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14 votes
0 answers
491 views

How can we deduce that a hydrogen atom is stable in relativistic QED?

Consider relativistic quantum electrodynamics (QED) with three quantum fields: the electromagnetic field $A_\mu$, one fermion field $\psi$ for electrons/positrons, and one fermion field $\psi'$ for ...
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13 votes
7 answers
2k views

Why doesn't an object, despite having a non-zero potential energy stored in it, fall by itself from the elevation?

When an object is at a certain height, it has some energy stored in it as we have done some work on it to get it to that height. So when it already has energy, then why doesn't it fall off from the ...
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13 votes
4 answers
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Two planets in same orbit - not planets?

Let us pretend for a moment that there are two identical planets that are exactly opposite their star from each other and are the same distance from said star. (This would make them, at all times, ...
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13 votes
4 answers
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Is it possible that 5 planets can revolve around a single star in a single orbit?

I'm writing a novel and I'm quite confused if this system could be possible in the real universe. Is it possible that a system exist, where 5 identical planets which could be of same characteristics (...
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12 votes
2 answers
730 views

Is this a correct demonstration for why elements above untriseptium cannot exist?

With the confirmation that elements 113, 115, 117, and 118 are indeed fundamental elements that are now to be named on the periodic table, the next question is: what is the highest atomic number ...
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12 votes
2 answers
645 views

Stable muon density inside a white dwarf star?

It occurs to me (though I'm hardly the first) that the decay $$ \mu^- \to e^- + \bar \nu_e + \nu_\mu $$ should be forbidden in electron-degenerate matter, since there must be an empty state available ...
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12 votes
2 answers
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Is Dyson Sphere a stable construction?

Suppose that a star is encompassed by a Dyson Sphere. Do we need a position control system for the Dyson Sphere to keep its origin always aligned with the center of the star? Will it stay aligned ...
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12 votes
2 answers
368 views

Is there a connection between Bertrands theorem and Chaos theory?

Bertrand's theorem states Among central force potentials with bound orbits, there are only two types of central force potentials with the property that all bound orbits are also closed orbits, ...
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11 votes
2 answers
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How is stable levitation possible?

This question is with reference to the video in this blog post: http://www.universetoday.com/90183/quantum-levitation-and-the-superconductor/ My question is the following: how is the disc stable in ...
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11 votes
1 answer
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How "large" is a Lagrange point?

When placing an object at a L-point, the natural assumption, as with all things gravity, is that you needn't place it in an exact spot to achieve a stable configuration. How much room do you have to ...
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11 votes
1 answer
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The most stable way of standing in a bus

Here's what's bugging me for quite a long time. Imagine the every day situation, that you are standing in a bus with your back on wall having only limited space on the floor and no handle to hold. You ...
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10 votes
5 answers
3k views

How can I prove that a state of equilibrium is unstable?

In the particular problem I encountered, an electric field was zero at the origin and we were meant to prove that a particle at the origin was in an unstable state of equilibrium. Is it enough to ...
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10 votes
2 answers
610 views

Why is the number of isotopes of an element bounded?

Is there a known reason why any given element has finitely many isotopes? Here I mean both stable and unstable isotopes. If we know this, do we have a reason why, for a given element, are the isotopes ...
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10 votes
6 answers
8k views

Why a system should be at its lowest energy state for its stability?

Every possible reaction in chemistry is to attain stability. In physics, the alignment of an electric dipole in an external electric field and in all other physical systems (at least those I study in ...
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10 votes
3 answers
4k views

What if the Moon was 100x more massive: Binary planets?

I was reading a couple of Earth-Moon related questions (Mars just collided with Earth! A question of eccentricity, Could the earth have another moon?) and they got me thinking about planet-moon ...
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10 votes
4 answers
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Question on the stability of the solar system

One of the pertinent questions about many body systems that causes me much wonder is why the solar system is so stable for billions of years. I came across the idea of "resonance" and albeit an useful ...
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10 votes
3 answers
1k views

How fast do you have to spin an egg to have it standing?

If you take a hardboiled egg and put it on a table and start to spin it, if you spin it fast enough it will start to spin in an upright position. What is the angular velocity needed for this ...
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10 votes
1 answer
580 views

Why does a book leaned up against a wall sometimes fall over after being stable for many hours?

This problem has been vexing me for years. Sometimes, you lean a book up against a wall and it stays there (the static frictional force balancing gravity, etc), but then after a long time (hours or ...
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