2 votes

Stokes' theorem and vector continuity equations

As an example of the physical meaning behind such manipulations; Faraday's law is of the form of your first differential relation: $$\nabla\times\vec E+{\partial\vec B\over\partial t}=0.$$ We can ...
Albertus Magnus's user avatar
2 votes
Accepted

Poynting's theorem and continuity equation

Continuity equations like the ones you are concerned with always arise whenever one attempts to mathematically formulate a notion of the local conservation of some quantity. The physical ...
Albertus Magnus's user avatar
2 votes
Accepted

Do we know that energy of a system is conserved if no external forces do work on it?

The work energy theorem is essentially a statement that energy is conserved whenever there are no non-conservative external forces acting on a system. This is so because in order for work to be done ...
Albertus Magnus's user avatar
2 votes

Integrable many-body system and complete set of conserved charges

"Remarks on the notion of quantum integrability" (JS Caux and J Mossel, Journal of Statistical Mechanics: Theory and Experiment 2011, no. 02, 2011), Sec. 5 mentions with regard to the ...
lm1909's user avatar
  • 21
2 votes

Noether Charge and Gauge Fields

The abelian case: The Lagrangian $$ \mathcal{L} = F^{\mu\nu} F_{\mu\nu} $$ is invariant off shell under local gauge symmetry $$ A_\mu(x) \mapsto A_\mu (x) - \partial_\mu \theta(x) $$ The Noether ...
zixuan feng's user avatar
1 vote

What happens if an object hits stationary objects on a pulley?

In a collision, if two objects stick together kinetic energy cannot be the same before and after the collision. This is why it is called a perfectly inelastic collision. There is some force that does ...
BioPhysicist's user avatar
  • 56.5k
1 vote

Conservation of Momentum in particle splitting. Is it always conserved?

In your second case, if the round mass moves to the right then it must be that some of the components of the explosive move to the left at high velocity in order to conserve momentum.
Not_Einstein's user avatar
  • 2,766
1 vote
Accepted

Jump conditions and energy flux between moving block and floor

The flux of mechanical energy, $\pmb{n}\cdot \pmb{\tau}\cdot \pmb{u}$, is still valid at any surface where all of the variables are well defined. So as you approach the discontinuity from one side you ...
Dale's user avatar
  • 100k

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