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6.6. Relativistic impulse

Lecture



The equations of classical mechanics are invariant with respect to the Galilean transformations, but with respect to the Lorentz transformations they turn out to be non-invariant. From the theory of relativity, it follows that the equation of dynamics, invariant with respect to the Lorentz transformations, has the form:

  6.6.  Relativistic impulse

Where   6.6.  Relativistic impulse - invariant, i.e. the same value in all reference systems called the particle's rest mass, v- particle velocity,   6.6.  Relativistic impulse - force acting on the particle. Compare to the classical equation.

  6.6.  Relativistic impulse

We conclude that the particle’s relativistic impulse is

  6.6.  Relativistic impulse (6.7)

Relativistic mass.

Determining the particle mass m as the coefficient of proportionality between speed and momentum, we obtain that the particle mass depends on its speed.

  6.6.  Relativistic impulse (6.8)

Energy in relativistic dynamics.

For particle energy in the theory of relativity, the expression is obtained:

  6.6.  Relativistic impulse (6.9)

From (2.3) it follows that a particle at rest possesses energy

  6.6.  Relativistic impulse (6.10)

This value is called the particle rest energy. Kinetic energy is obviously equal

  6.6.  Relativistic impulse (6.11)

Considering that   6.6.  Relativistic impulse , the expression for the total energy of a particle can be written as

  6.6.  Relativistic impulse (6.12)

From the last expression it follows that the energy and mass of the body are always proportional to each other. Any change in body energy   6.6.  Relativistic impulse accompanied by a change in body weight

  6.6.  Relativistic impulse

and, conversely, any change in mass   6.6.  Relativistic impulse accompanied by a change in energy   6.6.  Relativistic impulse . This statement is called the law of the relationship or the law of proportionality of mass and energy.

created: 2014-09-13
updated: 2021-03-13
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Physical foundations of mechanics

Terms: Physical foundations of mechanics