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

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1answer
151 views

Relationship between local and global scaling (Weyl) symmetry

Theorem 5.1 on page 80 of this paper says that Assuming that the matter fields satisfy their equations of motion, the matter field action is locally Weyl invariant if and only if the corresponding ...
4
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2answers
494 views

How to apply Noether's theorem

Say I have a point transformation: $$x' ~=~ (1 +\epsilon)x,$$ $$t' ~=~ (1 +\epsilon)^2t,$$ and Lagrangian $$ L ~=~ \frac{1}{2}m\dot{x}^2 - \frac{\alpha}{x^2}.$$ How do I go out about showing ...
20
votes
6answers
2k views

Can Noether's theorem be understood intuitively?

Noether's theorem is one of those surprisingly clear results of mathematical calculations, for which I am inclined to think that some kind of intuitive understanding should or must be possible. ...
2
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3answers
2k views

Proving angular momentum is conserved for a particle moving in a central force field $\vec F =\phi(r) \vec r$

A problem I am trying to work out is as follows: A particle moves in a force field given by $\vec F =\phi(r) \vec r$. Prove that the angular momentum of the particle about the origin is constant. ...
4
votes
1answer
557 views

How does Delta baryon decay conserve angular momentum?

I'm a chemist so bear with me: I understand the Delta baryons $\Delta^{+}$ and $\Delta^{0}$ to be in some sense spin (and isospin) quartet states of the proton and neutron. These can decay straight ...
0
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1answer
176 views

Analysis of the impulse of 2 colliding carts under the effect of magnetic repulsion

Hi there! I have a question about an experiment that was conducted. It is related to momentum. 2 carts were put on a track on opposite sides. They were then propelled towards one another at ...
2
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2answers
265 views

Thermal expansion is an expression of which conservation laws?

Many objects get larger as they heat up and contract as they cool down. Which conservation laws are applied to describe this phenomenon? How do they interact with each other to produce this effect?
2
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2answers
328 views

Rotation, cats landing on their feet, and conservation of angular momentum

Let θ be the orientation (angle) of a body (such as a cat), and let ω be its angular velocity. It is well-known that θ can change even when the body is not rotating, using the conservation of angular ...
0
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1answer
577 views

What is the linear momentum of an inelastic and elastic collision?

The arrows in the figure represent the linear momentum of two balls before they collide. If the collision is perfectly inelastic, find the linear momentum after the collision. If the collision is ...
1
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1answer
175 views

Conservation of momentum with MOND

Assuming as true the phenomenological MOND law for low accelerations ($< 10^{-10} m s^{-2} = a_0$), and considering a small mass $m$ attached to a larger mass $M$ by a faint spring (let's think of ...
2
votes
2answers
178 views

Is there any law that prevents an object with mass to become massless?

I got into a discussion with my physics teacher about the speed of light and I asked What if an object with mass was to lose mass as it gained speed-- would that allow for an object to eventually ...
0
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1answer
122 views

Non-relativistic Kepler orbits

Consider the Newtonian gravitational potential at a distance of Sun: $$\varphi \left ( r \right )~=~-\frac{GM}{r}.$$ I write the classical Lagrangian in spherical coordinates for a planet with mass ...
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1answer
2k views

Violation of Newton's 3rd law and momentum conservation

Why and when does newtons 3rd law violate in relativistic mechanics? Check this link http://www.animations.physics.unsw.edu.au/jw/Newton.htm.
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2answers
233 views

Conservation of Linear Momentum with respect to a given direction

Is linear momentum conserved in any direction? More specifically, if you project all momentum vectors in a system onto another vector, will momentum be conserved? I know that momentum is conserved ...
1
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2answers
2k views

Inelastic collision and conservation of linear and angular momentum

Is it possible for two spheres (a & b) to have an inelastic collision with BOTH the total linear and angular momentum preserved? I'm doing some physics simulation of some spheres attracting each ...
2
votes
1answer
322 views

Why has the trace of the energy-momentum tensor to vanish for conserved scaling currents to exist?

In this paper, the authors say that the trace of the energy-momentum tensor has to vanish to allow for the existence of conserved dilatation or scaling currents, as defined on p 10, Eq(22) $$ ...
3
votes
3answers
760 views

Newton's 3rd Law: How can I break things?

If I punch a wooden board hard enough and it breaks in two, has the board still exerted a force of equal magnitude on my fist? When the board breaks in two due to my force, the halves have a ...
1
vote
1answer
480 views

How did one get the defining equation of probability current and conservation of probability current and density?

I'm reading the Wikipedia page for the Dirac equation: $$\rho=\phi^*\phi$$ and this density is convected according to the probability current vector $$J = ...
3
votes
3answers
418 views

Conservation of Energy in Different Frames of Reference

Say I have a bucket of fuel that can produce 150J of energy by combustion. No matter what frame of reference an observer or the bucket of fuel is in, since the configuration of molecules stay the ...
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3answers
252 views

Interaction between a Pair of Particles

We consider a particle, A receiving energy from a second one,particle B in a one dimensional collision. $$E^2=p^2+m_0^2$$ $$EdE=pdp$$ For particle A: $$E_AdE_A=p_Adp_A{\;\;\;\;\;\;}(1)$$ For ...
12
votes
5answers
2k views

What is the conserved quantity of a scale-invariant universe?

Consider that we have a system described by a wavefunction psi(x). We then make an exact copy of the system, and anything associated with it, (including the inner cogs and gears of the elementary ...
3
votes
2answers
268 views

Can a neutron be created from pure energy

Is it possible to create a neutron out of pure energy, i.e. not by bringing a bunch of already-existing quarks together? (A quick calculation using E = mc2 shows the energy required would be about 1.5 ...
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1answer
212 views

Improved energy-momentum tensor

While still dealing with this issue, I've stumbled upon this answer to a question asking about the conserved quantity corresponding to a scaling transformation. It mentions that in accordance with ...
2
votes
1answer
611 views

What is a Pseudoscalar particle?

Can someone explain to me what is a pseudoscalar particle? And how do experiments figure out that what they're dealing with is a scalar or pseudoscalar?
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2answers
333 views

How can a non-conservative field be a scalar multiple of a conservative field?

Okay so I was reading this from University Physics by Freeman and Young and on the topic of inductors as circuit element, they wrote that $\mathbf{E_c} + \mathbf{E_n} = 0$ which makes no sense to me ...
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1answer
733 views

Scattering problem: Converting the two-body lab frame problem into a one-body center-of-mass frame problem

I'm reading the section on scattering in Goldstein's Classical Mechanics, and I have a rather basic question about this. It says that scattering in the laboratory is a two-body problem because of ...
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2answers
196 views

Having Trouble With The Principle Of Conservation Of Momentum For a Multiparticle System

I'am reading John Taylor's Classical Mechanics chapter 1 page 20 where he proves the principle of conservation of momentum which states "If the net external force $F^{ext}$ on an $N$-particle system ...
2
votes
1answer
520 views

Conservation of angular momentum across different reference frames?

I saw the following problem from the USAPhO: A uniform pool ball of radius $r$ begins at rest on a pool table. The ball is given a horizontal impulse $J$ of fixed magnitude at a distance $\beta r$ ...
0
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1answer
179 views

Charge-less, Mass-less, Spin Fields

after looking through a couple QFT texts it seems that all the spin-1/2 fields come associated with a charge of some sort. I was wondering if it's possible to write down a classical lagrangian (with ...
2
votes
3answers
222 views

Should any theory of physics respect the principle of conservation of angular momentum or linear momentum?

Is it possible that a theory that can describe the universe at the planck scale can violate things that we now consider fundamental in nature?For example can it violate rotational and translational ...
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2answers
158 views

What is the origin of nonconservative force?

My understanding about conservative force is a force that its work is independent of path such that we can construct another form of the work called potential to make our life easier. For friction, ...
4
votes
1answer
254 views

Lepton Number Conservation

What is the global symmetry of the electroweak Lagrangian that gives rise to lepton number conservation? As I understand it, electric charge is some linear combination of the conserved quantities ...
0
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3answers
1k views

Will a stone thrown in space move forever?

If I throw a stone on space, in a place where gravity is equal zero, will the stone move forward forever, because no air, so no friction?
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2answers
503 views

Conservation of momentum equation, how do I factor out v0Final and v1Final?

I am trying to figure out an equation for conservation of momentum. So, If combined momentum before and after the collision is the same, and momentum is velocity times mass, then for 2 objects (A,B), ...
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5answers
1k views

Is the converse of Noether's first theorem true: Every conservation law has a symmetry?

Noether's (first) theorem states that any differentiable symmetry of the action of a physical system has a corresponding conservation law. Is the converse true: Any conservation law of a physical ...
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votes
3answers
1k views

How do the Planets and Sun get their initial rotation?

How do the Planets and Sun get their initial rotation? Why do Venus and Mercury rotate so slowly compared to other planets and why does Venus rotate in a different direction to Mercury, Earth and ...
4
votes
2answers
387 views

Would a sneeze by a cosmonaut in a spacesuit affect his movement?

Naive question; feel free to shoot me down It is a truism that any motion in space would continue indefinitely unless it is opposed by an external force. If a cosmonaut were to sneeze within his/her ...
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1answer
248 views

How to determine n equidistant vectors from point P in three dimensions

As an assignment for uni I need to figure out an algorithm that explodes a particle of mass $m$, velocity $v$, into $n$ pieces. For the first part of the assignment, the particle has mass $m$, ...
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votes
1answer
603 views

Question on Impulse-Momentum theory

A 5kg stone kicked by a student undergoes a velocity change from 6m/s to 10m/s in 4 seconds; ---- What is the momentum change of the stone within the time interval? ---- What impulse ...
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votes
1answer
125 views

Could a people do all sort of gymnastics movement in vacuum space? [closed]

Could a people do all sort of gymnastics movement in vacuum space? I asked this because I am worry about that the astronaut leave the space shuttle during emergency could not go back to earth by ...
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1answer
194 views

Mathematical question on Collisions [closed]

A 2.5kg ball travelling with a speed of 7.5m/s makes an elastic collision with another ball of ...
0
votes
1answer
102 views

Period of an Object in Periodic Motion

My attempt (if it matters): The initial period is given by $T_X = \frac{2\pi X}{v}$ for some $v$. The new period is given by $T_Y = \frac{2\pi Y}{v}$ for the same $v$. $Y = \frac{X}{2}$, so ...
10
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1answer
394 views

Neutrino Oscillations and Conservation of Momentum

I would like to better understand how neutrino oscillations are consistent with conservation of momentum because I'm encountering some conceptual difficulties when thinking about it. I do have a ...
6
votes
1answer
371 views

Effect of the tail of the cat in the falling cat problem

To explain why a falling cat can turn by 180 degree without external torque and without violation of the conservation of angular momentum, one usually models the cat as two cylinders as in ...
6
votes
3answers
677 views

How does $F = \frac{ \Delta (mv)}{ \Delta t}$ equal $( m \frac { \Delta v}{ \Delta t} ) + ( v \frac { \Delta m}{ \Delta t} )$?

That's how it's framed in my Physics school-book. The question (or rather, the explanation) is that of the thrust of rockets and how the impulse is equal (with opposite signs) on the thrust-gases and ...
1
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1answer
261 views

Rocket drive and conservation of momentum

I am currently reading through some lecture notes of Physics 1 and in a chapter about the dynamics of the mass point, there is an example covering the rocket drive. Let $v$ be the velocity of the ...
3
votes
0answers
100 views

Videos of changing the orientation of an astronaut in space

Kane, Headrick and Yatteau describe in their paper "Experimental investigation of an astronaut maneuvering scheme" possible maneuvers to change the orientation in space without external torque. Is ...
2
votes
1answer
209 views

How to express the heat capacity in terms of heat?

The first law of thermodynamics divides the internal energy change into contributions of heat and work. $$\text dU=\omega_Q-\omega_W,$$ Here I chose the notation to emphasise that the two parts are ...
3
votes
1answer
184 views

Any case of a particle seemingly decaying into copies of itself?

Is there any case reported that seems to resemble the following: there is a particle and at some moment, the particle seems to break down into two or more particles that are all identical to the ...
5
votes
3answers
3k views

Why can't a single photon produce an electron-positron pair?

In reading through old course material, I found the assignment (my translation): Show that a single photon cannot produce an electron-positron pair, but needs additional matter or light quanta. ...