Questions tagged [conservation-laws]

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

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Why change in momentum in vertical motion in a projectile not zero? [closed]

My answer is $$mv\sqrt{2}$$. I neglected the change in x component and just subtracted the initial y component of momentum with the negative(Rule of Coordinate system) of the same and computed the ...
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Conservation of charge and quantisation of charge

How does the idea of conservation of charge relate to the quantisation of charge.
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What does Conservation of momentum mean in Quantum mechanics?

In quantum mechanics why do we say that momentum in conserved when different measurements on particle give different values of it ? For example in ground state of Harmonic oscillator I know that ...
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Conservation of angular momentum using symmetry properties

Goldstein pg 59 It can be shown that if a cyclic coordinate $q_{j}$ is such that $d q_{j}$ corresponds to a rotation of the system of particles around some axis, then the conservation of its ...
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Fully developed flow in cylinder coordinates

I have a flow that is: steady (time derivative is zero) fully developed in-compressible (constant density) no slip at the wall axis-symetric (theta derivative is zero) The configuration of the pipe ...
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Physical interpretation of Klein-Gordon Equation conserved charge

In the Klein-Gordon Equation the conserved charge is: $$\rho = \frac{i \hbar}{2m} (\psi^* \frac{\partial \psi}{\partial t} - \frac{\partial \psi^*}{\partial t} \psi) $$ rather than the conserved (...
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Conservation of Momentum Paradox Thought-Experiment (Please Explain) [closed]

The Device: Imagine a physical system involving two circular rings of distinct inner and outer radii, but equal in inertia. The smaller ring is superimposed inside the inner radius of the larger ring. ...
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Newton's Principia Naturalis: question on Corollary III?

I'm reading Newton's Principia Naturalis and have a question on Corollary III p86: The quantity of motion, which is collected by taking the sum of the motions directed towards the same parts, and ...
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Is momentum conserved in our current cosmological models?

The cosmological principle states that the universe, on large enough scales, is homogenous and isotropic. Noether's theorem says that space-translational invariance corresponds to conservation of ...
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Global conservation + Lorentz invariance = local conservation?

On the page 83 of "Quantum Field Theory Lectures of Sidney Coleman", Coleman showed an interesting example: It seems that global conservation law and local conservation law can be related. ...
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The principle of conservation of electric charge (or law of conservation of electric charge) $\iff \sum_{i=1}^n q_i=0$?

The principle of conservation of electric charge (or law of conservation of electric charge) affirms that: in a closed (isolated) system, which does not exchange any matter with the outside, the ...
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Change in angular velocity of an initially non-rotating spherical object after a collision

In the theoretical scenario below: Will the object rotate? My first thoughts on this were: The initial angular velocity is $0$. This means it does not have any angular momentum (right...?) and it ...
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Are there any fusion reactions that reduce the number of baryons?

In the simplest of fusion reactions, two hydrogen nuclei fuse to form deuterium. Besides deuterium, we get a positron and an electron neutrino out of it. The positron combines with the extra electron ...
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A situation where mass and energy are separately conserved?

I know that in a closed system mass+energy is always conserved. For example, in an exothermic reaction, some mass is converted to energy. Now, I'm looking for a situation where mass and energy are ...
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Problem similar to Feynman disk paradox. (violation of conservation of angular momentum)

I have a problem(paradox) similar to Feynman disk paradox. There is a example similar to Feynman disk paradox in Griffiths electrodynamics. Example 8.4 shows that the initial angular momentum of ...
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Why should momentum be conserved in special relativity?

This is more of a philosophical question than an actual physics question, but I don't see a clear reason why relativistic momentum, or energy for that matter, should be conserved. The equivalence ...
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If the light was slowing down universally could we detect it? What do we need? [duplicate]

Is there a way to detect it if light was slowing down universally, i.e. if speed of light $c$ in vacuum was getting smaller? Edit I was directed to this question. But I did not find the answer I ...
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Intuition behind torque, rotational inertia and angular momentum

I'm reading about conservation of linear momentum and angular momentum. I understand the idea that angular momentum should be thought of as the "rotational analogue" of linear momentum, just ...
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Conserved quantity from a conserved current

In my QFT course, it was asserted that the conserved quantity associated with some conserved current is given by $Q = \int_v j^0d^3x$ where $j^0$ is the time component of the conserved current, and $d^...
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What are some examples of multiplicative quantum numbers?

Wikipedia does not have much on its page for multiplicative quantum numbers, so I was wondering if there was a list or something somewhere?
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How do "chameleon particles" conserve energy and momentum?

I recently learned about the Chameleon particle model for dark energy, which involves bosonic particles whose mass changes depending on the nearby matter concentration, such that their mediated force ...
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Can we "see" why the Einstein tensor has zero divergence?

Is it possible to draw some kind of picture to illustrate why the Einstein tensor has zero divergence? I would guess not, because the only curved manifolds we can fully visualize are 2D surfaces with ...
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Conservation of Momentum - Rocket

I was wondering why the mass of the fuel is regarded as -dm and the mass of the rocket as m+dm? I understand that the total mass has to be unchanged (ie m). Why can't I say that the rocket's mass is m-...
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What is the conversion ratio of linear to angular momentum when a ball hits a rod in space?

If the ball hits the rod at 90 degrees then the rod will start spinning, while also following the original trajectory of the ball. On what factors does the ratio between the two types of momentum ...
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Different derivations of first Noether's theorem [duplicate]

I'm my current studies in Noether's theorem, the two that I liked the most are joshphysics answer to this Phys SE. post, and the derivation in chapter $4$ of An Elementary Introduction to Classical ...
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Will the change in kinetic energy during projectile motion always zero?

Will the change in kinetic energy i.e. $\frac{1}{2}mv^2-\frac{1}{2}mu^2$ always zero in case of projectile motion since the initial speed and final speed is the same that is $u$? If my observation is ...
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Does the theory of the Conservation of motion apply to horizontal-vertical systems?

Suppose, a trolley is moving along a frictionless surface with a constant velocity. After some time a mass is added to the trolley. I read somewhere that the theory of Conservation of motion will ...
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Why Goldstein's book is claiming that radius and angle doesn't contain time variable even there is $\dot{r}$ and $\dot{\theta}$?

$$L=\frac{1}{2}m(\dot{r}^2+r^2\dot{\theta}^2)-V(r)$$ $$p_\theta=\frac{\partial L}{\partial \theta}=mr^2\dot{\theta}$$ $$\dot{p}_\theta=\frac{d}{dt}(mr^2\dot{\theta})$$ Goldstein wrote that $\dot{P}_\...
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Proof of Newton's Third Law

Recently, I started thinking about how to prove or, at least, provide an intuitive explanation for why Newton's third law should be true, and I found this article: https://www.lockhaven.edu/~dsimanek/...
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What is the physical reasoning behind the generation of equal but opposite force (Newton's third law)?

When I apply a force on a body, it will apply a force on me (Newton's third law). But where does this force on me (i.e. equal but opposite force) generate from? Does it generate from within the body, ...
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What is the difference between objectivity and symmetry?

I encounter this question when reading a paper about continuum mechanics (Kumar and Parks, 2015, Proc.R.Soc.A. refer to eq.3.1 and eq.3.3) Speaking of the objectivity of strain energy density ${\psi}$,...
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Some help in understanding energy conservation relating to special relativity

Consider the decay of particle $A$ into particles $B$ and $T$ where $T$ is the tachyon particle. The conservation of energy equation can thus be expressed as $$m_A=\sqrt{p^2+m^2_B}-\sqrt{p^2-m^2_T}\,.$...
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How is energy conservation & Noether's theorem a non-trivial statement?

Noether's theorem says that energy conservation is a result of temporal translation symmetry of the laws of physics. This is implied to be - and I'm not saying it's not - a very non-trivial statement. ...
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Principle of least action to prove that conservation of momentum results from translational symmetry

In an article that I am reading http://go.owu.edu/~physics/StudentResearch/2005/LauraBecker/SymmetrytoConservation.html - the author proves, firstly, why translational symmetry in space results from ...
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Is there a physical reason behind electromagnetic energy and momentum being derived from the Lorentz force equation?

The effect of the EM field upon a charge $q$ is given by the relativistic Lorentz force equation: $$\frac{dP}{d\tau}= qF^{\alpha\beta}U_{\beta}$$ The expression on the RHS is then substituted via ...
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Derivation of Noether's theorem by Gateaux derivative

Noether's theorem states that if: $$\ \int_{a}^{b} F(x, y, y') \,dx = \ \int_{a_{new}}^{b_{new}} F(x_{new}, y_{new}, y_{new}') \,dx_{new} $$ for any $a$, $b$ and $y(x)$, and when $x$ and $x_{new}$ ...
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Energy conservation as non-time-dependence in SIMPLE terms

In Berkeley Physics Course volume 1 on Mechanics, on page 144 it says "The law of conservation of energy states that for a system of particles with interactions not explicitly$^1$ dependent on ...
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How can the momentum be conserved in $y$ direction here?

In this question, A circus acrobat of mass $M$ leaps straight up with initial velocity $v_0$ from a trampoline. As he rises up, he takes a trained monkey of mass $m$ off a perch at a height $h$ above ...
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Can every global conservation law be written as following? [duplicate]

Consider a physical quantity $\phi$ that is globally conserved. From Feynman's argument (in his volume 2 I think), which states that local conservation follows from global conservation due to special ...
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Newtonian vs Lagrangian symmetry

Suppose we have a ball of mass $m$ in the Earth's gravitational field ($g=const.$). Equation of motion reads as: $$ ma = -mg $$ From here we can conclude that we have translational symmetry of the ...
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How can the entropy of an isolated system possibly change (if we consider the fundamental equation)?

By the definition of an isolated system, $dE = dN = dV = 0$ (energy, no. of particles, and volume). If we assume that a macrostate has a unique ($E$, $V$, $N$) then we can write $$dS = \frac1T\cdot dE ...
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How can a marble on a circular track return to its point of origin using only its own momentum?

A marble rolling on a curved track appears to violate conservation of momentum. Please help me understand why this is illusion and/or what mechanism is acting such that momentum is cancelled and ...
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What does $\frac{\partial}{\partial t}\delta(\mathbf{r}-\mathbf{r}_k)$ equal to?

How do we get the gradient in the RHS of (2.15), where $\mathbf{r}_k(t)$ is the position of the moving particle? This is from page 32 in Zangwill's electrodynamics textbook: Let $N$ point charges $...
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Application of conservation of momentum to this system has absurd implications

The system, everything shown in the picture (table, pulley, spring, string, blocks, wall), was initially at rest, with spring unstretched. Friction is absent everywhere, and spring, string, and pulley ...
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General formula for collisions involving rotation?

I am trying to write a 2d game engine involving collisions of convex polygons. Using the basic formula for elastic collisions I am able make my shapes collide realistically only considering their ...
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Man moving on a frictionless plank

A person of mass $m$ is standing on one end of a frictionless plank of mass $M$ and length $L$ and floating in the water. The person moves from one end to another and stops. The displacement of the ...
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Momentum and angular momentum during a car turn

Imagine a car speeds up to some speed then shuts off the engine, then does a 90 degree turn, then moves forward again without ever switching the engine back on, so that any steering is done only with ...
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Can a rocket keep moving forever in outer space even if its no longer using fuel? [duplicate]

Can a rocket use just enough fuel to reach an area wherein it has escaped a planet's gravitational pull and then turn its engine off? Supposing there is nothing else with a gravitational pull that the ...
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Final speed of a two block system [closed]

Suppose a large block $M$ is moving in a smooth surface with speed $v_o$. Then a smaller block $m$ is carefully placed on it. Find the final speed I tried two methods which gave two different answers ...
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How is energy conserved in this system?

In space, a photon with momentum $P_1$ is reflected off a mirror, accelerating it slightly. Now there is a reflected photon with momentum $P_2$ in the other direction. So, the mirror must have ...

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