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1answer
24 views

What does the g mean after the isotope given?

I'm familiar with notation such as Sc-44m standing for the meta stable state of Sc-44. What does Sc-44g mean? There are a few examples of this notation; here's one: ...
4
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1answer
55 views

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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2answers
142 views

Why don't electrons collide among themselves

The Heisenberg principle states that we cannot ascertain simultaneously the position or momentum of any small particle. However slight, is there a chance that 2 or more electrons from the same or ...
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0answers
10 views

Examples of systems with stable equilibria on the boundary of the phase space

An example of bounded gradient flows are Hopfield networks, which are gradient dynamical systems, used (among other things) to solve combinatorial optimization problems, because stable equilibria are ...
4
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2answers
177 views

Rayleigh-Taylor Instability dependence on acceleration direction

I'm trying to bolster my understanding of the Rayleigh-Taylor instability, and I've gotten stuck on the point of which fluid (more or less dense) is being accelerated into the other. Cases of uniform ...
1
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1answer
31 views

Stability and Laplace's equation

Consider four positive charges of magnitude $q$ at four corners of a square and another charge $Q$ placed at the origin. What can we say about the stability at this point? My attempt goes like this. ...
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2answers
42 views

A particles lifetime in relation to the speed it travels with

Is it possible for a particles or any matter's lifetime in the universe to depend on it's speed?
4
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1answer
143 views

Deducing instability growth rates from the Hamiltonian for the nonlinear schrodinger equation

Consider the following nonlinear Schrodinger equation (NLSE): $$A_t+iA_{xx}+i|A|^2A = 0$$ where $A$ is a complex valued function of $(x,t)$. A solution to this equation is $A=a_oe^{-ia_o^2t}$. We ...
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9answers
11k views

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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0answers
21 views

Initial conditions for second order ODE with complex stiffness

I tried this on Math Stack Exchange. I'm trying to find initial conditions to ensure systems of the form stay bounded $$\ddot{x}_i+\sum_{j=1}^N k_{ij} x_j = 0, \quad k_{ij} \in \mathbb{C}.$$ For ...
2
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1answer
49 views

Spinning rubber ball with equatorial ridge

I have this rubber ball with something like a very slight equatorial ridge (sort of like Saturn's moon Iapetus) which I often spin around on my desk. I keep noticing that no matter the inclination of ...
3
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0answers
42 views

Bottle stableness optimization

A few days ago me and some friends played a game where you need to upset a bottle with a ball(flunkyball). Then a question occured: "How much water do we need to put into the bottle that its ...
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0answers
18 views

The pressure profile of a static heap of granular substances

The following is the pressure profile of a pile of sand. Note that there is a pressure minimum at the center. A possible explanation for this is: Due to the close packing of the grains, any grain ...
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2answers
59 views

Why are L4 and L5 Lagrange points stable as points and not part of a circle?

I read this Phys.SE thread which is similar Why are L4 and L5 lagrangian points stable? but I did not want to necro that thread. It seems that most discussions of a three body problem are presented ...
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8answers
5k views

Why are L4 and L5 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 L1, L2, and L3 lagrangian points. The blue ...
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3answers
271 views

Why doesn't an orbiting body keep accelerating?

As a physics newbie I'm trying to get a grip on basic orbital mechanics. I think I'm beginning to get grasp on how bodies interact with each other. When a body approaches another body it accelerates ...
1
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2answers
52 views

Gravity effect on moving bodies

If we imagine two suns of equal mass, and a small object in their combined center of gravity, which is not moving, it will stay there forever. If the object is displaced a little bit towards one of ...
3
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1answer
247 views

Vacuum stability in quantum field theory

What exactly do people mean when they talk about the scale dependence of the effective potential ($V$)? I explain the motivation for my question (and hence my confusion) below. Please correct me as ...
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0answers
47 views

How stable is a tablespoon of neutrons once removed from a neutron star? [duplicate]

I've often heard public lectures describing the degenerate, exotic matter left behind after a star collapses but fails to go supernova; one that has found its way to become a neutron star. The speaker ...
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8answers
8k views

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?
3
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2answers
488 views

Deviation from Earth's orbit

How much orbital deviation is required for the Earth to get knocked out from current orbit so it either moves away from Sun or towards the Sun?
2
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1answer
58 views

Why should slope of pressure versus volume always be negative?

I read that the slope of the pressure, ($P$), versus volume ($V$) graph should always be negative for thermodynamic stability, but there was no further explanation in the text. Could someone give an ...
0
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3answers
114 views

What makes an orbit stable or unstable?

I have an assignement, where I have a given central potential $V(x)=-\frac{K}{6r^6}$ and object with an angular momentum $L$. I've calculate the radius of a circular orbit, which I've done by ...
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1answer
90 views

Classifying regions of Van der Waal like gas

Given the equation of state $$p+a\left(\frac{N}{V}\right)=\frac{Nk_BT}{V-bN} \tag 1$$ Taking into account of the fact that a realistic model requires $p \geq 0, V \geq Nb, N>0$ classify the ...
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2answers
1k views

Countersteering a motorcycle

Everyone knows the story about countersteering. For those who don't I will explain it below and after the explanation i will ask my question. You can watch this short video as a beginning: ...
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0answers
19 views

why can noise induce multistability, particularly in (bio)chemical systems

There are several instances that people claim that a system is monostable in a deterministic model, but when they consider stochastic models, from either master equations or Fokker-Planck equations, ...
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2answers
442 views

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 ...
35
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3answers
5k views

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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0answers
11 views

Recursion relations and stability analysis

I have a recursion relation in the form of the following two equations: $X_{t+1} = X_t + V_{t+1} \\ V_{t+1} = wV_t + cy(g-X_t)$ I want to write these two equations into a matrix form so that I can ...
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votes
2answers
250 views

Why are planets in unstable equilibrium in a stable orbit

It is well known that a planet in stable orbit is in unstable equilibrium. If e.g. the moon was just a few m/s slower in velocity, or a few m closer to the earth than it is, the gravity would ...
5
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1answer
141 views

Why is a hexagon such a stable shape for materials?

A hexagonal lattice is famously the shape of graphene, the source of the 2010 Nobel prize. The shape also shows up in beehives and in the basalt columns of Giant's Causeway in County Antrim. ...
1
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2answers
37 views

Notions of “confined” and “metastable” states?

What is the exact definition of terms "confined state" and "metastable state", in the context of quantum mechanics? Can we also have a "confined metastable state"? Can we somehow easily link these ...
0
votes
1answer
44 views

Is an elastic, gravitating object stable?

As I understand, an object can contract under its own gravitantional pull. Then as it does so, different parts of the object must move with some velocity. This in turn means that their relativistic ...
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4answers
16k 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 ...
2
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1answer
36 views

Coexistence at Lagrange points

I was wondering how precise the location of an object in a Lagrange point needs to be to maintain stability, since it seems that several natural objects (asteroids) exists together in some of these ...
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1answer
324 views

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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4answers
469 views

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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2answers
152 views

Mars and Jupiter colliding [duplicate]

I was going to post a comment on my own theory about Mars and Jupiter colliding, but I just read the rules and it breaks it...badly. I was looking for informal peer review. So my question is, has ...
0
votes
1answer
37 views

2D room with electron-point-charges (stability)

Is there a fast way to find out stable #"point charges" & constellation for this kind of Simulation. The 2D repeating itselve in each direction till infinity, so i've a kind of symetrie here. ...
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0answers
48 views

Measure of stability

Is there a measure of stability of different systems? What I mean by stability is the ability of a system to return to its original position, even when inputted with high amounts of energy. The more ...
0
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1answer
67 views

Temporal properties of a photon

Naively, one can attempt to consider the (impossible) light-speed inertial frame. From there you arrive at nonsense conclusions like 'the universe is flattened in the direction of travel' which must ...
3
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1answer
79 views

Earth-Sun Lagrange points L4/L5 existence

Why do Lagrange points L4 and L5 exist at all? Consider the mass of Jupiter equals 320 Earth masses, and distance from Lagrange point to Jupiter is about 4-6 A.U. We get that the gravity of Jupiter ...
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2answers
1k views

How, exactly, does a reaction wheel work?

Reaction wheels, mounted on spacecrafts and satellites, are used for precision attitude control. It is not clear to me how they can do this, though. My best guess is that when a motor accelerates a ...
1
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1answer
174 views

Why does graphene exist?

I started to read some articles on graphene and almost all say that graphene was discovered late because physicists thought it would be unstable. Despite this, I didn't found a clear explanation of ...
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0answers
252 views

Calculations to Determine Force Required for Gyroscopic Stabalization

I am currently undertaking a project involving gyroscopes, the aim of which is to stabilize a large object. I have read that gyroscopes work because of conservation of angular momentum, and if you ...
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0answers
42 views

Argument for stability of journal bearing via inertial and viscous forces?

As I understand a journal bearing, a rotor is levitated by hydraulic forces from the lubricant. While these are lots of studies on this subject, I can't manage to find a paper that coherently breaks ...
0
votes
1answer
109 views

Classical Mechanics - Potential Energy Function [closed]

Question The potential energy function of a particle of mass $m$ is: $$V(x) = \frac{cx}{x^2+a^2}$$ where c and a are positive constants. Qualitatively sketch $V$ as a function of $x$. Find two ...
2
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3answers
259 views

Unstable equilibrium in a pendulum

Consider a pendulum with a bob and a massless, rigid, hinged rod attached to the bob. The bob is at rest at the bottom most position. Neglecting friction, is it possible to impart such a velocity ...
2
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1answer
189 views

Earnshaw's theorem and springs

Earnshaw's theorem states that the Laplacian of the potential energy of a small charge moving through a landscape full of static negative and/or positive charges (and gravity) is zero. Thus you can't ...
2
votes
1answer
139 views

Is there always an equilibrium point in space for gravity?

For instance, for a two-body system, there will always be a point in-between the two in which the forces of gravity completely cancel, and if I were there then I would experience no net force. I ...