Search results
Results from the WOW.Com Content Network
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
The (Newtonian) kinetic energy of a particle of mass m, velocity v is given by = | | = (+ +), where v x, v y and v z are the Cartesian components of the velocity v.Here, H is short for Hamiltonian, and used henceforth as a symbol for energy because the Hamiltonian formalism plays a central role in the most general form of the equipartition theorem.
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.
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 ...
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 ...
Jun-ichi Ueda and Yoshiro Sadamoto have found [1] that as increases beyond , the effective mass of a spring in a vertical spring-mass system becomes smaller than Rayleigh's value and eventually reaches negative values at about . This unexpected behavior of the effective mass can be explained in terms of the elastic after-effect (which is the ...
Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!
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.