# Relativistic Momentum

Relativistic momentum, abbreviated as \( p \), is a concept in physics that takes into account the effects of special relativity when describing the motion of objects at speeds comparable to the speed of light. In classical mechanics, momentum is defined as the product of an object's mass and its velocity. However, when an object is moving at speeds that are a significant fraction of the speed of light, classical mechanics breaks down, and special relativity becomes necessary.

The Lorentz factor appears in various relativistic equations. The presence of this factor ensures that as the velocity of an object approaches the speed of light, its relativistic momentum does not become infinite, in contrast to what would be predicted by classical mechanics.

As an object's velocity gets closer to the speed of light, the relativistic effects become more pronounced, and classical mechanics no longer accurately describes its motion. Relativistic momentum is a correction to classical momentum that accounts for these effects and becomes increasingly important as velocities approach the speed of light.

## Relativistic Momentum formula |
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\(\large{ p = \frac{ m \; v }{ \sqrt{ \frac{1 \;-\; v^2}{c^2} } } }\) | ||

Symbol |
English |
Metric |

\(\large{ p }\) = relativistic momentum | \(\large{ \frac{lbm-ft}{sec} }\) | \(\large{ \frac{kg-m}{s} }\) |

\(\large{ m }\) = rest mass | \(\large{ lbm }\) | \(\large{ kg}\) |

\(\large{ c }\) = speed of light | \(\large{ \frac{ft}{sec} }\) | \(\large{ \frac{m}{s} }\) |

\(\large{ v }\) = velocity of the body | \(\large{ \frac{ft}{sec} }\) | \(\large{ \frac{m}{s} }\) |

Tags: Momentum