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This equation holds for a body or system, such as one or more particles, with total energy E, invariant mass m 0, and momentum of magnitude p; the constant c is the speed of light. It assumes the special relativity case of flat spacetime [ 1 ] [ 2 ] [ 3 ] and that the particles are free.
The γ factor approaches infinity as v approaches c, and it would take an infinite amount of energy to accelerate an object with mass to the speed of light. The speed of light is the upper limit for the speeds of objects with positive rest mass, and individual photons cannot travel faster than the speed of light. [39]
The magnitude, denoted by S, divided by the speed of light is the density of the linear momentum per unit area (pressure) of the electromagnetic field. So, dimensionally, the Poynting vector is S = power / area = rate of doing work / area = ΔF / Δt Δx / area , which is the speed of light, c = Δx / Δt, times ...
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 ...
The formula defines the energy E of a particle in its rest frame as the product of mass (m) with the speed of light squared (c 2). Because the speed of light is a large number in everyday units (approximately 300 000 km/s or 186 000 mi/s), the formula implies that a small amount of mass corresponds to an enormous amount of energy.
It is common in particle physics, where units of mass and energy are often interchanged, to express mass in units of eV/c 2, where c is the speed of light in vacuum (from E = mc 2). It is common to informally express mass in terms of eV as a unit of mass, effectively using a system of natural units with c set to 1. [3] The kilogram equivalent ...
In Newtonian mechanics, momentum (pl.: momenta or momentums; more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction.
Here we use the relativistic expression for linear momentum: =, where = / /. with being an object's (rest) mass, speed, and c the speed of light in vacuum. Then kinetic energy is the total relativistic energy minus the rest energy : E K = E − m 0 c 2 = ( p c ) 2 + ( m 0 c 2 ) 2 − m 0 c 2 {\displaystyle E_{K}=E-m_{0}c^{2}={\sqrt {(p{\textrm ...