Relativistic Momentum: Mass, Velocity & Lorentz Factor

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SUMMARY

The relativistic momentum is defined by the equation p = mvγ, where γ (the Lorentz factor) accounts for the effects of relativity at high velocities. The discussion clarifies that while some physicists prefer using invariant rest mass (m₀), the relativistic mass (mᵣ = γm₀) is also valid for calculating momentum at relativistic speeds. Both approaches are acceptable, and the choice depends on the context and preference of the physicist. Key texts on relativity provide further insights into these concepts.

PREREQUISITES
  • Understanding of the Lorentz factor (γ)
  • Familiarity with the concept of relativistic mass
  • Basic knowledge of momentum in classical mechanics
  • Awareness of invariant rest mass (m₀)
NEXT STEPS
  • Study the derivation of the Lorentz factor in special relativity
  • Explore the implications of relativistic mass on energy and momentum
  • Learn about the differences between relativistic and classical momentum
  • Review key texts on relativity, such as "Spacetime Physics" by Edwin F. Taylor and John Archibald Wheeler
USEFUL FOR

Students of physics, educators teaching relativity, and anyone interested in advanced mechanics and the implications of relativistic effects on mass and momentum.

khil_phys
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The relativistic momentum is given by p=mvγ, where Y is the Lorentz factor and m is the rest mass of the body.
My question is that if we are considering the momentum of the body at relativistic speeds, shouldn't we also consider the relativistic mass of the body?
 
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That's exactly what you are doing. It is just p = mr v, where m_\mathrm{r} = \gamma m_0 is the relativistic mass (in the direction of v).
 
Compu is right. Although you will find other physicists prefer to write the invariant rest mass, m_0, and \mathbf{u}=\gamma (c,\vec{v})=\gamma\mathbf{v}. You could find either of these in the various texts on relativity.
 

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