Relativistic Energy-Momentum Calculator
Relativistic Energy-Momentum Calculator finds energy and momentum of a particle, with a plot vs. velocity.
Formulas Used in Relativistic Energy-Momentum Calculator
The calculator computes the relativistic energy and momentum of a particle:
Lorentz Factor:
\\[ \gamma = \frac{1}{\sqrt{1 – \frac{v^2}{c^2}}} \\]Energy:
\\[ E = \gamma m c^2 \\]Momentum:
\\[ p = \gamma m v \\]Where:
- \\(\gamma\\): Lorentz factor
- \\(m\\): Rest mass (kg)
- \\(v\\): Velocity (m/s)
- \\(c\\): Speed of light (\\(2.99792458 \times 10^8 \, \text{m/s}\\))
- \\(E\\): Energy (J or eV)
- \\(p\\): Momentum (kg·m/s)
Example Calculation
Example: Electron (\\(m = 9.109 \times 10^{-31} \, \text{kg}, v = 0.5c\\))
\\[
\gamma = \frac{1}{\sqrt{1 – (0.5)^2}} \approx 1.1547
\\]
\\[
E = 1.1547 \times 9.109 \times 10^{-31} \times (2.99792458 \times 10^8)^2 \approx 3.07 \times 10^{-14} \, \text{J} \approx 0.192 \, \text{MeV}
\\]
\\[
p = 1.1547 \times 9.109 \times 10^{-31} \times 0.5 \times 2.99792458 \times 10^8 \approx 1.82 \times 10^{-22} \, \text{kg·m/s}
\\]