Relativistic momentum

Definition

Relativistic momentum is the momentum of an object taking into account the effects of special relativity. It is given by $p = \gamma mv$, where $\gamma$ is the Lorentz factor, $m$ is the rest mass, and $v$ is the velocity.

5 Must Know Facts For Your Next Test

1. Relativistic momentum increases more rapidly than classical momentum as an object's speed approaches the speed of light.
2. The Lorentz factor, $\gamma$, in relativistic momentum is defined as $\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}$.
3. Relativistic momentum reduces to classical momentum ($p = mv$) at low velocities (when $v << c$).
4. Conservation of momentum in relativistic mechanics still holds true and must account for relativistic effects.
5. As velocity approaches the speed of light, relativistic momentum approaches infinity.

Review Questions

• What happens to relativistic momentum as an object's velocity approaches the speed of light?
• How does relativistic momentum differ from classical momentum at high velocities?
• State the equation for calculating relativistic momentum and define each term.

Related terms

Lorentz Factor: $\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}$, a factor that accounts for time dilation and length contraction in special relativity.

Rest Mass: The mass of an object when it is at rest relative to an observer, denoted by $m_0$.

Special Relativity: A theory formulated by Albert Einstein that describes the physics of moving bodies at speeds close to the speed of light and incorporates time dilation and length contraction.