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The local conservation of non-gravitational linear momentum and energy in a free-falling reference frame is expressed by the vanishing of the covariant divergence of the stress–energy tensor. Another important conserved quantity, discovered in studies of the celestial mechanics of astronomical bodies, is the Laplace–Runge–Lenz vector.
The law is derived from the principles of conservation of mass and momentum of the air stream flowing through an idealized "actuator disk" that extracts energy from the wind stream. According to Betz's law, no wind turbine of any mechanism can capture more than 16/27 (59.3%) of the kinetic energy in wind
For example, the stress–energy tensor is a second-order tensor field containing energy–momentum densities, energy–momentum fluxes, and shear stresses, of a mass-energy distribution. The differential form of energy–momentum conservation in general relativity states that the covariant divergence of the stress-energy tensor is zero: T μ ...
In physics a conserved current is a current, , that satisfies the continuity equation =.The continuity equation represents a conservation law, hence the name. Indeed, integrating the continuity equation over a volume , large enough to have no net currents through its surface, leads to the conservation law =, where = is the conserved quantity.
The Wigner–Eckart theorem is a theorem of representation theory and quantum mechanics.It states that matrix elements of spherical tensor operators in the basis of angular momentum eigenstates can be expressed as the product of two factors, one of which is independent of angular momentum orientation, and the other a Clebsch–Gordan coefficient.
With the first assumption, conservation of momentum implies (for non-zero density) that =; whereas the second assumption doesn't necessary imply that ρ is constant. This second assumption only strictly requires that the time rate of change of the density is compensated by the gradient of the density, as in: ∂ ρ ∂ t = − u ⋅ ∇ ρ ...
Download as PDF; Printable version; In other projects Appearance. move to sidebar hide. From Wikipedia, the free encyclopedia. ... Law of conservation of momentum.
in the above relation for conservation of momentum, is the momentum flux density and plays a role similar to in Poynting's theorem. The above derivation assumes complete knowledge of both ρ {\displaystyle \rho } and J {\displaystyle \mathbf {J} } (both free and bounded charges and currents).