\[p=\gamma mv\]
Variables
prelativistic momentum (kg·m/s)
gamma[γ]Lorentz factor
mrest mass (kg)
vvelocity (m/s)
Description
What is this formula?
The relativistic momentum formula calculates the momentum of an object moving at speeds close to the speed of light. Unlike classical momentum, it includes the Lorentz factor to account for relativistic effects.
When to use it
Use this formula when analyzing particles, high-speed objects, accelerator physics, and special relativity problems where classical momentum is no longer accurate.
Example
Data:
Rest mass:
m=9.11×10^-31 kg
Velocity:
v=2.4×10^8 m/s
Lorentz factor:
γ=1.67
Formula:
p=γmv
Substitution:
p=(1.67)(9.11×10^-31)(2.4×10^8)
Result:
p=3.65×10^-22 kg·m/s
Applications
- Particle accelerators
- High-energy physics
- Special relativity
- Electron dynamics
- Astrophysics
- Relativistic mechanics