1.6.1 Momentum and impulse

Momentum: the quantity that says how hard something is to stop

Definition

Momentum

The product of an object's mass and its velocity.

p = m v

where $p$ is momentum in $m/s\text{kg}\,\text{m/s}$ , $m$ is mass in $kg\text{kg}$ and $v$ is velocity in $m/s\text{m/s}$ .

A loaded lorry crawling through a car park and a cricket ball flying off the bat are both difficult to stop, for opposite reasons: one has a huge mass, the other a large velocity.
Momentum is the single quantity that folds those two ideas together, so it tells you what it really takes to bring a moving object to rest.
Momentum is a vector. It points in the same direction as the velocity, so two objects can carry equal amounts of momentum in opposite directions.
Before any calculation, choose a positive direction and write down what you chose. Anything travelling the other way then has a negative velocity, and therefore a negative momentum.
Momentum has no special unit name of its own. Write it as $m/s\text{kg}\,\text{m/s}$ , which you may also see written as $s−1\text{kg}\,\text{m}\,\text{s}^{-1}$ .
A large momentum means that stopping the object needs a large force, a long time, or both. That link is made exact by impulse, below.

Impulse: force multiplied by the time it acts

Definition

Impulse

The product of a force and the time for which that force acts, which is equal to the change in momentum it produces.

\text{impulse} = F\Delta t = \Delta(mv)

where $F$ is the force in $N\text{N}$ , $Δt\Delta t$ is the time in $s\text{s}$ , and $Δ(mv)\Delta(mv)$ is the change in momentum in $m/s\text{kg}\,\text{m/s}$ .

The second half of that equation carries the physics: a resultant force acting for a time changes an object's momentum, and the impulse tells you by exactly how much.
A bigger force changes the momentum more. So does the same force acting for longer. Only the product of the two matters.
Impulse is measured in newton seconds, $s\text{N}\,\text{s}$ . Because impulse equals a change of momentum, $s\text{N}\,\text{s}$ and $m/s\text{kg}\,\text{m/s}$ are the same unit, and either is accepted for an impulse answer.
Impulse is a vector acting in the direction of the force, so a force applied backwards gives a negative change of momentum and slows the object down.
Rearranging gives $\dfrac{\Delta(mv)}{\Delta t}$ , which says that spreading a fixed change of momentum over a longer time makes the force smaller.
That single line explains crumple zones, airbags, crash mats and bending your knees as you land. Your change of momentum is already fixed by how fast you were moving, so the only way to survive it comfortably is to stretch out the contact time.

Common Mistake

Momentum is not a moment. A moment is force $×\times$ perpendicular distance from a pivot, measured in $m\text{N}\,\text{m}$ ; momentum is mass $×\times$ velocity, measured in $m/s\text{kg}\,\text{m/s}$ .
Momentum is not kinetic energy. Momentum is a vector using $v$ once; kinetic energy is a scalar using $v^2$ . Two objects can share the same momentum and have very different kinetic energies.
On a rebound, do not simply subtract the two speeds. The velocity reverses, so the change of momentum is larger than the momentum you started with. Writing $0.15 \times (12 - 8.0)$ instead of $0.15 \times (-8.0 - 12)$ is the single most common error here.
Impulse is measured in $s\text{N}\,\text{s}$ , never in $N/s\text{N/s}$ .

Exam technique

You are expected to recall $p = m v$ and $impulse=FΔt=Δ(mv)\text{impulse} = F\Delta t = \Delta(mv)$ without a formula sheet, so write the equation down first: that alone often scores a mark even if the arithmetic later goes wrong.
Convert grams to kilograms and milliseconds to seconds before substituting, because the equations only work in SI units.
State your positive direction in words, for example "taking motion to the right as positive", so your negative signs can be followed.
The final mark usually depends on the unit, and on giving a direction whenever the question asks for one. A bare number will not do.

Self review

State what is meant by the momentum of an object, and give its unit.
A $kg1200\ \text{kg}$ car travels at $m/s15\ \text{m/s}$ . Calculate its momentum.
Define impulse, and write the equation that links it to change in momentum.
Explain why a car with a crumple zone exerts a smaller force on its passengers in a crash.
A ball of mass $kg0.20\ \text{kg}$ arrives at a wall at $m/s6.0\ \text{m/s}$ and rebounds at $m/s4.0\ \text{m/s}$ . Calculate the magnitude of the change in its momentum.

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1.6.1 Momentum and impulse

Momentum: the quantity that says how hard something is to stop

Definition

Momentum

The product of an object's mass and its velocity.

p = m v

where $p$ is momentum in $m/s\text{kg}\,\text{m/s}$ , $m$ is mass in $kg\text{kg}$ and $v$ is velocity in $m/s\text{m/s}$ .

A loaded lorry crawling through a car park and a cricket ball flying off the bat are both difficult to stop, for opposite reasons: one has a huge mass, the other a large velocity.
Momentum is the single quantity that folds those two ideas together, so it tells you what it really takes to bring a moving object to rest.
Momentum is a vector. It points in the same direction as the velocity, so two objects can carry equal amounts of momentum in opposite directions.
Before any calculation, choose a positive direction and write down what you chose. Anything travelling the other way then has a negative velocity, and therefore a negative momentum.
Momentum has no special unit name of its own. Write it as $m/s\text{kg}\,\text{m/s}$ , which you may also see written as $s−1\text{kg}\,\text{m}\,\text{s}^{-1}$ .
A large momentum means that stopping the object needs a large force, a long time, or both. That link is made exact by impulse, below.

Impulse: force multiplied by the time it acts

Definition

Impulse

The product of a force and the time for which that force acts, which is equal to the change in momentum it produces.

\text{impulse} = F\Delta t = \Delta(mv)

where $F$ is the force in $N\text{N}$ , $Δt\Delta t$ is the time in $s\text{s}$ , and $Δ(mv)\Delta(mv)$ is the change in momentum in $m/s\text{kg}\,\text{m/s}$ .

The second half of that equation carries the physics: a resultant force acting for a time changes an object's momentum, and the impulse tells you by exactly how much.
A bigger force changes the momentum more. So does the same force acting for longer. Only the product of the two matters.
Impulse is measured in newton seconds, $s\text{N}\,\text{s}$ . Because impulse equals a change of momentum, $s\text{N}\,\text{s}$ and $m/s\text{kg}\,\text{m/s}$ are the same unit, and either is accepted for an impulse answer.
Impulse is a vector acting in the direction of the force, so a force applied backwards gives a negative change of momentum and slows the object down.
Rearranging gives $\dfrac{\Delta(mv)}{\Delta t}$ , which says that spreading a fixed change of momentum over a longer time makes the force smaller.
That single line explains crumple zones, airbags, crash mats and bending your knees as you land. Your change of momentum is already fixed by how fast you were moving, so the only way to survive it comfortably is to stretch out the contact time.

Common Mistake

Momentum is not a moment. A moment is force $×\times$ perpendicular distance from a pivot, measured in $m\text{N}\,\text{m}$ ; momentum is mass $×\times$ velocity, measured in $m/s\text{kg}\,\text{m/s}$ .
Momentum is not kinetic energy. Momentum is a vector using $v$ once; kinetic energy is a scalar using $v^2$ . Two objects can share the same momentum and have very different kinetic energies.
On a rebound, do not simply subtract the two speeds. The velocity reverses, so the change of momentum is larger than the momentum you started with. Writing $0.15 \times (12 - 8.0)$ instead of $0.15 \times (-8.0 - 12)$ is the single most common error here.
Impulse is measured in $s\text{N}\,\text{s}$ , never in $N/s\text{N/s}$ .

Exam technique

You are expected to recall $p = m v$ and $impulse=FΔt=Δ(mv)\text{impulse} = F\Delta t = \Delta(mv)$ without a formula sheet, so write the equation down first: that alone often scores a mark even if the arithmetic later goes wrong.
Convert grams to kilograms and milliseconds to seconds before substituting, because the equations only work in SI units.
State your positive direction in words, for example "taking motion to the right as positive", so your negative signs can be followed.
The final mark usually depends on the unit, and on giving a direction whenever the question asks for one. A bare number will not do.

Self review

State what is meant by the momentum of an object, and give its unit.
A $kg1200\ \text{kg}$ car travels at $m/s15\ \text{m/s}$ . Calculate its momentum.
Define impulse, and write the equation that links it to change in momentum.
Explain why a car with a crumple zone exerts a smaller force on its passengers in a crash.
A ball of mass $kg0.20\ \text{kg}$ arrives at a wall at $m/s6.0\ \text{m/s}$ and rebounds at $m/s4.0\ \text{m/s}$ . Calculate the magnitude of the change in its momentum.

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Teach Genie

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1.6.1 Momentum and impulse

Momentum: the quantity that says how hard something is to stop

Impulse: force multiplied by the time it acts

Review 1.6.1 Momentum and impulse by teaching Genie

1.6.1 Momentum and impulse Revision Guide

1.6.1 Momentum and impulse

Momentum: the quantity that says how hard something is to stop

Impulse: force multiplied by the time it acts

Review 1.6.1 Momentum and impulse by teaching Genie

1.6.1 Momentum and impulse Revision Guide