The statement that a property of a system does not change if the system is isolated.

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Reason behind the rotation of Earth? [duplicate]

I want to know what is the reason that the Earth rotates on its own axis? What are the forces responsible for the Earth's rotation?
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28 views

$G$-parity in an electromagnetic decay

I am looking at the decay $\eta\rightarrow\pi^+\pi^-\gamma$ and I would assume that the decay itself (ignoring the $\pi\pi$ final state interaction that is obviously strong) is electromagnetic since ...
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91 views

How can a planet gravitationally capture objects?

I would expect that any asteroid or other object originating far away but passing near a planet would pick up speed and energy as it approaches, but unless it comes into contact with the atmosphere ...
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1answer
37 views

Integrals of Motion for s Degrees of Freedom

From Landau & Lifshitz, Classical Mechanics, the number of integrals of independent integrals of motion for a system of $s$ degrees of freedom is $2s-1$. I am considering a spherical pendulum in ...
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75 views

Particle number conservation equals $U(1)$-symmetry?

If have by now frequently read the above but never really understood it. It is said that the particle number conservations is related to the phase of the wave function, but how?
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2answers
50 views

A spring with two masses in an inelastic collision

An ideal spring is attached to a wall, and the other end is attached to a mass $m$. The spring is initially compressed a distance $x$. After it is released, the mass collides with another mass $2m$ ...
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74 views

Conservation laws and continuity equations

I'm a bit messed up with conservation laws and continuity equations. This is my understanding: A conservation law describes that a physical quantity $G$ is conserved with time. It does not prevent ...
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1answer
38 views

Relativistic Conservation laws [closed]

Conservation of Relativistic mass and thus energy is easily proven by considering an inelastic collision of two bodies while invoking the conservation of momentum. As such the momentum law appears ...
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3answers
295 views

Conservation of momentum but not kinetic energy in inelastic collisions

In inelastic collisions, the kinetic energy of the system is not conserved but the momentum is. Kinetic energy is: $0.5 \times \text{mass} \times \text{velocity}^2$. Momentum is: ...
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67 views

Will I be able to push a small object in front of me in the outer space?

Imagine I am standing on Earth, and pushing a tennis ball away from me. The ball moves. If it is very heavy, I will move back instead of the ball. Now consider the same scenario in outer space, where ...
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3answers
49 views

Why is momentum conserved in an inelastic collision and kinetic energy is not conserved?

We know that in an inelastic collision that total momentum of the system before collision equals the total momentum after collision. But total kinetic energy before collision is not equal to total ...
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4answers
115 views

What do you exactly mean when you say that momentum is conserved?

I am taking for granted that when we say that something is conserved it is understood 'in its full integrity'. Energy is represented by a number (of J, or other) and is usually conserved. But ...
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1answer
47 views

Relationship of multiple particles under collision [closed]

Consider 3 particles. All 3 particles travel along the x-axis. The 1st particle possesses some mass, m, and its initial position is somewhere on the negative x-axis. It has some (positive) velocity ...
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14 views

Relationship of multiple particles under collision [closed]

Consider 3 particles. All 3 particles travel along the x-axis. The 1st particle possesses some mass, m, and its initial position is somewhere on the negative x-axis. It contains some (positive) ...
2
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1answer
62 views

Conservation of linear momentum, when is it conserved?

Will Linear momentum be conserved in a non-inertial frame of reference? In other words what is the fundamental condition for linear momentum to be conserved? Also which is more fundamental- Newton's ...
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2answers
80 views

The charm of the gyroscope [closed]

I am fascinated by the gyroscope, like everyboy who was so lucky as to get such a toy as a kid. But probably also grown-ups are not immune to its charm. I am not asking for a theoretical explanation. ...
2
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1answer
102 views

Angular momentum, what is it, is it conserved, and how do we know?

Firstly, most definitions of angular momentum assume a point about which you define angular momentum. I realize that you can consider the angular momentum about any point, and have many angular ...
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33 views

Conserved charge from conserved current associated with translational invariance

(c.f Di Francesco, 'Conformal Field Theory' P.45) Di Francesco calls the conserved charge arising from the conserved current associated with a translation invariant theory the 'four momentum'. While ...
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1answer
37 views

Angular Momentum Conservation Definition [duplicate]

Did I missed something in angular momentum definition? Two identical bodies rotate around mass center. Now I invented anti-gravity and turning gravitational switch off. Those two bodies will move now ...
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1answer
61 views

Conservation in space-time curvature

Pardon this possibly naive question. I'm starting to poke around in the topic of General Relativity (as soon as I can pull myself back up out of the vortex of underlying mathematics that I've gotten ...
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1answer
94 views

When I move my arm forward in vacuum, will my body move backward?

Let's say I stay at point $x=0$ in vacuum. When I move my arm forward such that it will have a positive $x$ position (say $x=5$) will the rest of my body move backward such that it will have a ...
4
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1answer
93 views

Crystal Momentum in a Periodic Potential

I'm working through some basic theory on periodic potentials, and I would appreciate help in understanding the crystal momentum. Suppose we have a Bravais lattice with lattice vectors $\textbf{R}$. ...
2
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1answer
35 views

Deriving conserved currents by promoting parameter

I currently reading Tong's text on String Theory. In Chapter 4.1.1 he alludes to a technique to derive conserved currents Recall that we can usually derive conserved currents by promoting the ...
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2answers
68 views

If a ball spinning on a rod hits another ball, what is conserved linear or angular momentum?

Suppose a 1-kg ball A is fixed to a spoke 0.2 m long, which is attached to an axle so that the ball can rotate (v=10m/s, KE=50J, $\omega$=50 rps, L=2, p=0) Now, there is a second ball B (m=1kg), ...
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1answer
32 views

Conserved current for a constant translation of a free massless scalar field

In Zinn-Justin's Quantum Field Theory and Critical Phenomena they start with an action for a free massless scalar field: $$S(\varphi) = \frac{1}{2}\int ...
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3answers
309 views

Does the the quantum field theoretic process of particle–antiparticle annihilation break the axioms of Special Relativity?

$\textbf{Note that this diagram hasn't anything to do with the question directly.}$ After a particle and its antiparticle annihilate, their energy is converted into a force carrier particle, such ...
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27 views

Gravitational force and time dilation [closed]

Suppose the radius of the earth is reduced by half but the mass is same, then how long will it take to complete one rotation, 24, 48, 12 or 6 h.? please give the mathematical relations and solution. ...
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1answer
93 views

What's the point of NASA's impossible space engine? Wouldn't a mirror work better?

My understanding (which is very little) is that the point of NASA's recent virtual-particle engine is to convert solar energy into momentum. That's fine, but what's the point? If the spacecraft is ...
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693 views

NASA's “Impossible” Space Engine

Recently, there was some news that said that the researchers at NASA have come across some impossible kind of space engine which does not require any fuel. I have read at a few places like here, here ...
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1answer
60 views

Finding direction of a ball after collision in cartesian coordinate system [closed]

In elastic collision of ball to wall along x axis m*Vix=m*Vfx as velocity of wall is 0 before and after collision thus Vix=Vfx ......eq(1) Kinetic Energy is conserved so m*Vi2 = m*Vf2 (Vix2 + ...
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How obtain conserved quantities in integrable models in accordance with Liouville's theorem, via Sklyanin Poisson algebra?

In classical integrable models, in the discrete case we have the Sklyanin algebra, $$\lbrace T_{a}(u),T_{b}(v)\rbrace =[r_{ab}(u,v),T_{a}(u)T_{b}(v)].$$ How to prove that the conserved quantities are ...
3
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0answers
53 views

What's the corresponding symmetry of enstrophy conservation?

In fluid mechanics, especially 2D turbulence study, people talk about conservation of enstrophy. But I can't really understand enstrophy very well, and what's the corresponding symmetry of enstrophy ...
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1answer
52 views

Please explain the flaw in this picture [duplicate]

So I saw this picture on my google+ feed and I immediately know why it wont work. But I'm having trouble explaining to myself and others exactly why. Without using anything overly complex, can anyone ...
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3answers
952 views

What determines whether a pool ball will bouce backwards after colliding with another pool ball?

I'm no knowledgeable pool player, but I've noticed that sometimes when the cue ball hits another pool ball, they roll together; and sometimes the cue ball bounces back. And I have a very, very rough ...
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4answers
160 views

How to calculate a collision which is partly elastic and partly inelastic?

(For the purpose of this question, "calculating a collision" means: given the velocities and masses of two objects in a collision, figuring out the new velocities of both objects after the collision). ...
3
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1answer
131 views

Hamiltonian Noether's theorem in classical mechanics

How does one think about, and apply, Noether's theorem in the classical mechanical Hamiltonian formalism? From the Lagrangian perspective, Noether's theorem (in 1-D) states that the quantity ...
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1answer
81 views

Conservation of energy and momentum via the continuity equation in asymmetric time and space translation

I am confused about energy and momentum conservation, time and space translation symmetry, and the continuity equation. Suppose we have a mass $m$ in inertial space far from any gravitational ...
3
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4answers
294 views

Is the principle of Conservation of Energy empirically verifiable?

Before I am inundated by myriad and vociferous claims that conservation of energy is the single most well-attested and experimentally verified principle in all of science, let me say that I am well ...
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2answers
71 views

Color-charge conservation in proton decay

In some extensions of the Standard Model of particle physics (Supersymmetry with R-parity violation being a prominent example), the proton is allowed to decay, e.g. via $p\to e^+\pi^0$: While this ...
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2answers
74 views

Why is scattering vector $\vec{q}$ called vector of 'momentum transfer'?

In the world of scattering the angle at which you detect the scattered radiation is known as $q$, where $$ \vec{q} = \frac{4\pi\eta}{\lambda}\sin(\theta/2) $$ I read in a lot of books that this is ...
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1answer
67 views

Reversing Noether's theorem [duplicate]

Noether's theorem states: any differentiable symmetry of the action of a physical system has a corresponding conservation law. Is this statement invertible? I mean, if a conservation law exists, this ...
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3answers
106 views

Conservation of 4-momentum in special relativity

I understand that the inner product of two 4-vectors is conserved under the Lorentz transformations, so that the absolute value of the four momentum is the same in any reference frame. This is what I ...
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Association of financial phenomena/indications with the conservation laws of Black Scholes equation

For a while I've been doing research on methods of obtaining conservation laws via the symmetries of differential equations (DEs). I'm presently doing research on identifying financial ...
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1answer
198 views

Relationship between the continuity equation and the wave equation

What exactly is the relationship between the continuity equation and the wave equation? Suppose $J^\mu$ is a contravariant vector that satisfies the continuity equation $\partial_\mu J^\mu=0$. Let ...
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1answer
44 views

What factors indicates inelastic collision?

I am watching this example from Wikipedia: I am wondering what factors would indicate that the collision of 2 objects will be inelastic (I know macroscopic scale impacts are never perfectly ...
0
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1answer
39 views

Velocity change of objects

Is it possible for small object (small mass, let's say bullet) to hit large object (big mass, let's say rock) and still move forward (or stop) instead of being reflected (let's say objects don't crush ...
3
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1answer
73 views

Euler Equations, Sod shock tube & conservation

Conservation of momentum? I am considering the Euler equations in conservative form and solving the Sod shock tube problem I have written a Godunov finite volume type solver. It solves for density ρ, ...
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2answers
67 views

Calculating velocity change after impact?

Let's say there is no gravity here and objects won't crush. We have 2 rocks with $m=10\text{ kg}$. First rock has velocity $v_1=0\text{ m/s}$ and second $v_2=10\text{ m/s}$ (flying in leftward ...
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2answers
48 views

Jump of a mass and violation of physical laws

I've just watched one of Feynman's lectures on the character of physical law where he was talking about conservation laws. In that particular part he was reasoning why a mass can't "jump" from one ...