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## Class 11 Physics (India)

### Course: Class 11 Physics (India)>Unit 9

Lesson 14: Introduction to linear momentum and impulse

# Linear momentum review

Overview of key terms and equations for linear momentum, including a derivation of Newton's second law from the conservation of linear momentum.

## Key terms

Term (symbol)Meaning
Linear momentum ($p$)Product of an object's mass and velocity. Also called “momentum” for short. Momentum is conserved when no external forces act on a system. Vector quantity with SI units of $\frac{\text{kg}\cdot \text{m}}{\text{s}}$.

## Equations

EquationSymbolsMeaning in words
$p=mv$$p$ is momentum, $m$ is mass, and $v$ is velocityMomentum is mass times velocity.
$\mathrm{\Delta }p={F}_{\text{net}}\mathrm{\Delta }t$${F}_{\text{net}}$ is the net external force, $\mathrm{\Delta }p$ is change in momentum, and $\mathrm{\Delta }t$ is the time over which a net force actsChange in momentum is proportional to the net external force and 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 $\mathrm{\Delta }v$ can also be written as $a\mathrm{\Delta }t$. We can then see that any change in momentum following an acceleration can be written as
$\begin{array}{rl}\mathrm{\Delta }p& =m\mathrm{\Delta }v\\ & =m\left(a\mathrm{\Delta }t\right)\\ & ={F}_{\text{net}}\mathrm{\Delta }t\end{array}$
If we rearrange this to solve for ${F}_{\text{net}}$ when the mass of the system and net force is constant, we get Newton’s second law
${F}_{\text{net}}=\frac{\mathrm{\Delta }p}{\mathrm{\Delta }t}$
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!

## Common mistakes and misconceptions

1. 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.
2. 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.