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The Lorentz factor γ is defined as [3] = = = = =, where: . v is the relative velocity between inertial reference frames,; c is the speed of light in vacuum,; β is the ratio of v to c,; t is coordinate time,
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
If v = 0 we have the identity matrix which coincides with putting v = 0 in the matrix we get at the end of this derivation for the other values of v, making the final matrix valid for all nonnegative v. For the nonzero v, this combination of function must be a universal constant, one and the same for all inertial frames.
If the body's speed v is much less than c, then reduces to E = 1 / 2 m 0 v 2 + m 0 c 2; that is, the body's total energy is simply its classical kinetic energy ( 1 / 2 m 0 v 2) plus its rest energy.
The following notations are used very often in special relativity: Lorentz factor = where = and v is the relative velocity between two inertial frames.. For two frames at rest, γ = 1, and increases with relative velocity between the two inertial frames.
A polyatomic gas, like water, is not radially symmetric about any axis, resulting in D = 6, comprising 3 translational and 3 rotational degrees of freedom. Because the equipartition theorem requires that kinetic energy is partitioned equally, the total kinetic energy is K = D K t = D 2 N m v 2 . {\displaystyle K=DK_{\text{t}}={\frac {D}{2}}Nmv ...
An EasyJet flight heading to England was forced to make an emergency landing in Greece after the pilot reportedly collapsed.. The aircraft was traveling from Hurghada, Egypt to Manchester, England ...
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.