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At a low speed (v ≪ c), the relativistic kinetic energy is approximated well by the classical kinetic energy. To see this, apply the binomial approximation or take the first two terms of the Taylor expansion in powers of v 2 {\displaystyle v^{2}} for the reciprocal square root: [ 14 ] : 51
In classical mechanics, both the m 0 c 2 term and the high-speed corrections are ignored. The initial value of the energy is arbitrary, as only the change in energy can be measured and so the m 0 c 2 term is ignored in classical physics. While the higher-order terms become important at higher speeds, the Newtonian equation is a highly accurate ...
Its initial value is 1 (when v = 0); and as velocity approaches the speed of light (v → c) γ increases without bound (γ → ∞). α (Lorentz factor inverse) as a function of velocity—a circular arc. In the table below, the left-hand column shows speeds as different fractions of the speed of light (i.e. in units of c). The middle column ...
where the factor of 2 arises because the metric is a symmetric tensor, and the convention of Latin indices i, j taking space-like values 1, 2, 3 is used. As each component of the metric has space and time dependence in general; this is significantly more complicated than the formula quoted at the beginning, see metric tensor (general relativity ...
The relativistic Lagrangian can be derived in relativistic mechanics to be of the form: = (˙) (, ˙,). Although, unlike non-relativistic mechanics, the relativistic Lagrangian is not expressed as difference of kinetic energy with potential energy, the relativistic Hamiltonian corresponds to total energy in a similar manner but without including rest energy.
Continuous charge distribution. The volume charge density ρ is the amount of charge per unit volume (cube), surface charge density σ is amount per unit surface area (circle) with outward unit normal n̂, d is the dipole moment between two point charges, the volume density of these is the polarization density P.
Let us assume a static, spherically symmetric perfect fluid. The metric components are similar to those for the Schwarzschild metric: [2] = = By the perfect fluid assumption, the stress-energy tensor is diagonal (in the central spherical coordinate system), with eigenvalues of energy density and pressure:
An electronvolt is the amount of energy gained or lost by a single electron when it moves through an electric potential difference of one volt.Hence, it has a value of one volt, which is 1 J/C, multiplied by the elementary charge e = 1.602 176 634 × 10 −19 C. [2]