Summarizing Relativistic Momentum

Relativistic Momentum Summary

• The law of conservation of momentum is valid whenever the net external force is zero and for relativistic momentum. Relativistic momentum \(p\) is classical momentum multiplied by the relativistic factor \(\gamma \).
• \(p=\text{γmu}\), where \(m\) is the rest mass of the object, \(u\) is its velocity relative to an observer, and the relativistic factor \(\gamma =\cfrac{1}{\sqrt{1-\cfrac{{u}^{2}}{{c}^{2}}}}\).
• At low velocities, relativistic momentum is equivalent to classical momentum.
• Relativistic momentum approaches infinity as \(u\) approaches \(c\). This implies that an object with mass cannot reach the speed of light.
• Relativistic momentum is conserved, just as classical momentum is conserved.

Glossary

relativistic momentum

\(p\), the momentum of an object moving at relativistic velocity; \(p=\text{γmu}\), where \(m\) is the rest mass of the object, \(u\) is its velocity relative to an observer, and the relativistic factor \(\gamma =\cfrac{1}{\sqrt{1-\cfrac{{u}^{2}}{{c}^{2}}}}\)

rest mass

the mass of an object as measured by a person at rest relative to the object