Linear momentum: Difference between revisions

Latest revision as of 19:55, 20 January 2010

Definition

For a single body in pure translation

The linear momentum of a body is the vector $m \bar{v}$ , where $m$ is the mass of the body and $\bar{v}$ 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 $n$ bodies with masses $m_{1}, m_{2}, \dots, m_{n}$ respectively and velocities ${\bar{v}}_{1}, {\bar{v}}_{2}, \dots, {\bar{v}}_{n}$ respectively, the total linear momentum is given by:

$\sum_{i = 1}^{n} m_{i} {\bar{v}}_{i}$

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:

$\int \bar{v} d m$

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

$\int \bar{v} ρ d V$

Units and dimensions

Question	Answer
Scalar or vector?	Vector
Instantaneous or time-cumulative	Instantaneous
MLT dimensions	$M L T^{- 1}$ : MLT;1;1;-1 (same as those of impulse)
SI units	$k g m / s$ (kilograms meter per second) or $N - s$ (Newton-second)

@@ Line 22: / Line 22: @@
 <math>\int \overline{v} \rho \, dV</math>
+==Units and dimensions==
+{| class="sortable" border="1"
+! Question !! Answer
+|-
+| Scalar or vector? || [[Quantity type::Vector]]
+|-
+| Instantaneous or time-cumulative || [[Quantity type::Instantaneous]]
+|-
+| MLT dimensions || <math>MLT^{-1}</math>: [[MLT::MLT;1;1;-1]] (same as those of [[impulse]])
+|-
+| SI units || <math>kgm/s</math> (kilograms meter per second) or <math>N-s</math> (Newton-second)
+|}