Linear momentum

Linear momentum is a vector quantity defined as the product of an object's mass, m, and its velocity, v. Linear momentum is denoted by the letter p and is called “momentum” for short: Note that a body's momentum is always in the same direction as its velocity vector. The units of momentum are kg. · m/s.

Equations

Equation	Symbols	Meaning in words
$p = mv$p, equals, m, v	$p$p is momentum, $m$m is mass, and $v$v is velocity	Momentum is mass times velocity.
$\Delta p = F_\text {net} \Delta t$delta, p, equals, F, start subscript, n, e, t, end subscript, delta, t	$F_\text {net}$F, start subscript, n, e, t, end subscript is the net external force, $\Delta p$delta, p is change in momentum, and $\Delta t$delta, t is the time over which a net force acts How momentum and net force are related You might recall from the kinematic equations with constant acceleration that change in velocity $\Delta v$delta, v can also be written as $a \Delta t$a, delta, t. We can then see that any change in momentum following an acceleration can be written as $\begin{aligned} \Delta p &= m\Delta v \\ &= m(a\Delta t)\\ &= F_\text {net} \Delta t \end{aligned}$ If we rearrange this to solve for $F_\text {net}$F, start subscript, n, e, t, end subscript when the mass of the system and net force is constant, we get Newton’s second law $F_\text {net} = \dfrac{\Delta p}{\Delta t}$F, start subscript, n, e, t, end subscript, equals, start fraction, delta, p, divided by, delta, t, end fraction Thus, the change in momentum over time is equal to the net force. A bigger net force over the same time period means a larger change in momentum. For example, a heavy truck coming to a stop will have a much larger change in momentum than a light car in the same amount of time. A larger change in momentum means a larger external force is needed to slow it down, so the truck brakes have to work much harder! [Is net force the same as the average force?] $F_\text {net}$F, start subscript, n, e, t, end subscript$F$F$F_\text {ave}$F, start subscript, a, v, e, end subscript Common mistakes and misconceptions Some people think momentum and kinetic energy are the same. They are both related to an object’s velocity (or speed) and mass, but momentum is a vector quantity that describes the amount of mass in motion. Kinetic energy is a measure of an object’s energy from motion, and is a scalar. Sometimes people think momentum is the same as force. Forces cause a change in momentum, but momentum does not cause a force. The bigger the change in momentum, the more force you need to apply to get that change in momentum.	Change in momentum is proportional to the net external force and the time over which a net force acts.