Definition:Linear Momentum/Relativistic Model
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Definition
A more accurate model for the linear momentum of a body is given by:
- $\mathbf p = \gamma m \mathbf v$
where $\gamma$ is the Lorentz factor:
- $\gamma = \dfrac c {\sqrt {c^2 - v^2} } = \dfrac 1 {\sqrt {1 - v^2 / c^2} }$
where:
- $c$ is the speed of light in vacuum
- $v$ is the magnitude of $\mathbf v$: $v = \size {\mathbf v}$
It is clear $\gamma \approx 1$ (and thus that $\mathbf p \approx m \mathbf v$) for values of $v$ much less than $c$.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Newton's laws of motion
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Newton's laws of motion