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Plots of (γ − 1)c 2 × mass, versus proper velocity × mass, for a range of mass values along both axes. Plotting "( γ − 1) versus proper velocity" after multiplying the former by mc 2 and the latter by mass m , for various values of m yields a family of kinetic energy versus momentum curves that includes most of the moving objects ...
The total (mechanical) force that is calculated to induce the proper acceleration on a mass at rest in a coordinate system that has a proper acceleration, via Newton's law F = ma, is called the proper force. As seen above, the proper force is equal to the opposing reaction force that is measured as an object's "operational weight" (i.e. its ...
where u is the velocity of the ejected/accreted mass as seen in the object's rest frame. [17] This is distinct from v, which is the velocity of the object itself as seen in an inertial frame. This equation is derived by keeping track of both the momentum of the object as well as the momentum of the ejected/accreted mass (dm).
The history of an object traces a curve in spacetime, called its world line. If the object has mass, so that its speed is necessarily less than the speed of light, the world line may be parametrized by the proper time of the object. The four-velocity is the rate of change of four-position with respect to the proper time along the curve. The ...
Rest energy (also called rest mass energy) is the energy associated with a particle's invariant mass. [2] [3] The rest energy of a particle is defined as: =, where is the speed of light in vacuum. [2] [3] [4] In general, only differences in energy have physical significance. [5]
The proper length of an object is the length of the object in the frame in which the object is at rest. ... (x 1, x 2, x 3) ... m = invariant mass . Velocity 3 ...
In classical mechanics, the kinetic energy of a non-rotating object of mass m traveling at a speed v is . [2] The kinetic energy of an object is equal to the work, or force in the direction of motion times its displacement , needed to accelerate the mass from rest to its stated velocity.
Stellar proper motions have been used to infer the presence of a super-massive black hole at the center of the Milky Way. [18] This now confirmed to exist black hole is called Sgr A*, and has a mass of 4.3 × 10 6 M ☉ (solar masses). Proper motions of the galaxies in the Local Group are discussed in detail in Röser. [19]