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## Class 11 Physics (India)

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

Lesson 14: Introduction to linear momentum and impulse

# Impulse review

Overview of key terms and equations related to impulse, including how impulse can be calculated from a force vs. time graph.

## Key terms

Term (symbol)Meaning
Impulse ($F\mathrm{\Delta }t$)Product of the average force exerted on an object and the time interval during which the force is exerted. Impulse is equal to the change in momentum ($\mathrm{\Delta }p$) and is sometimes represented with the symbol $J$. Vector quantity with SI units of $\text{N}\cdot \text{s}$ or $\frac{\text{kg}\cdot \text{m}}{\text{s}}$.

## Equations

EquationSymbolsMeaning in words
$\mathrm{\Delta }p={F}_{\text{net}}\mathrm{\Delta }t$$\mathrm{\Delta }p$ is the change in momentum, ${F}_{\text{net}}$ is the net force, and $\mathrm{\Delta }t$ is the time period of the net forceImpulse is proportional to the constant net force acting on an object and the time period that the net force acts.

## How force changes momentum

If we take the impulse equation and solve for force, another relationship of the equation presents itself:
$\begin{array}{rl}F\mathrm{\Delta }t& =\mathrm{\Delta }p\\ \\ F& =\frac{\mathrm{\Delta }p}{\mathrm{\Delta }t}\end{array}$
When a net force is exerted on an object, it changes that object's momentum over the time of the force exertion. In other words, force is the rate at which momentum changes. For example:
• If an object experiences a large momentum change ($\mathrm{\Delta }p$) over a short time duration ($\mathrm{\Delta }t$), then there must have been a large net force ($F$) applied to it.
• Conversely, if an object experiences a small momentum change ($\mathrm{\Delta }p$) over a long time duration ($\mathrm{\Delta }t$), then there must have been a small net force ($F$) applied to it.

## How to find impulse from a force vs. time graph

Impulse is the area under the curve of the force vs. time graph. Areas above the time axis are positive $\mathrm{\Delta }p$ and areas below the axis are negative $\mathrm{\Delta }p$. If the force is not constant, we can divide the graph into sections and add up the impulse in each section.
For example, to find the total impulse on the object in the force vs. time graph in Figure 1 over ${t}_{1}+{t}_{2}$, the areas of ${A}_{1}$ and ${A}_{2}$ can be added together.
${A}_{1}$ is a rectangle of height ${F}_{0}$ and width ${t}_{1}$. ${A}_{2}$ is a triangle of height ${F}_{0}$ and base ${t}_{2}$. The total impulse on the object over ${t}_{1}+{t}_{2}$ is
$\begin{array}{rl}\mathrm{\Delta }p& ={A}_{1}+{A}_{2}\\ \\ \\ & ={F}_{0}{t}_{1}+\frac{1}{2}{F}_{0}{t}_{2}\end{array}$
For worked examples of finding impulse or change in momentum from a force vs. time graph, watch our video about calculating impulse from force vs. time graphs.

## Common mistakes and misconceptions

1. People forget what the sign of impulse means. Impulse is a vector, so a negative impulse means the net force is in the negative direction. Likewise, a positive impulse means the net force is in the positive direction.
2. People mistake impulse with work. Both impulse and work depend on the external net force, but they are different quantities. The properties of impulse and work are compared in the table below.
ImpulseWork
Product of net force and...timedisplacement
Changes an object’smomentumenergy
Quantity typevectorscalar