# Linear momentum

From Mech

## Contents

## Definition

### For a single body in pure translation

The **linear momentum** of a body is the vector , where is the mass of the body and is the velocity of the body.

### For a system of bodies, each in pure translation

The **linear momentum** of a system is the sum of the linear momenta of all the bodies in that system. If the system comprises bodies with masses respectively and velocities respectively, the total linear momentum is given by:

This is a vector summation.

### For a single body undergoing motion that is not purely translation

In this case, we integrate the velocity vector over a mass differential:

This is equivalent to integrating the product of velocity and density over a volume differential:

## Units and dimensions

Question | Answer |
---|---|

Scalar or vector? | Vector |

Instantaneous or time-cumulative | Instantaneous |

MLT dimensions | : MLT;1;1;-1 (same as those of impulse) |

SI units | (kilograms meter per second) or (Newton-second) |