5.7.1 Momentum is a property of moving objects

Momentum

Definition

Momentum

Momentum is the product of an object's mass and its velocity.

Every moving object has momentum because it has both mass and a velocity.

A stationary object has a velocity of

m/s0\ \text{m/s}

, so its momentum is

m/s0\ \text{kg m/s}

Momentum is a vector, so it has a size and a direction, pointing the same way as the velocity.

Momentum is calculated from

p = m v

, where

p

is momentum in

m/s\text{kg m/s}

m

is mass in

kg\text{kg}

and

v

is velocity in

m/s\text{m/s}

For the same velocity, a greater mass gives greater momentum.

For the same mass, a greater velocity gives greater momentum.

If either the mass or the velocity doubles while the other stays the same, the momentum doubles.

Calculating momentum

To find momentum, put the mass in

kg\text{kg}

and the velocity in

m/s\text{m/s}

into

p = m v

Convert grams to

kg\text{kg}

and

km/h\text{km/h}

m/s\text{m/s}

before substituting.

You can rearrange

p = m v

when the momentum is known: use

\dfrac{p}{v}

to find mass, or

\dfrac{p}{m}

to find velocity.

Example

A car of mass $kg1200\ \text{kg}$ travels at $m/s15\ \text{m/s}$ . Calculate its momentum.

State the equation: $p = m v$ .
Substitute the values: $\times 15$ .
Calculate the answer: $18\,000\ \text{kg m/s}$ .

Example

An object has momentum $m/s54\ \text{kg m/s}$ and mass $kg6.0\ \text{kg}$ . Calculate its velocity.

State the equation: $p = m v$ .
Rearrange for velocity: $\dfrac{p}{m}$ .
Substitute the values: $\dfrac{54}{6.0}$ .
Calculate the answer: $9.0\ \text{m/s}$ .

Common Mistake

Do not confuse momentum with force: momentum is measured in $m/s\text{kg m/s}$ , never in newtons.
Always use mass in $kg\text{kg}$ ; if it is given in grams, divide by $1000$ first.
Always use velocity in $m/s\text{m/s}$ , not $km/h\text{km/h}$ .

Exam technique

Write $p = m v$ before substituting, so you can still earn the equation mark if the arithmetic slips.
Show any rearrangement, substitute with units, and give the answer in $m/s\text{kg m/s}$ .

Self review

What is momentum?
What is the equation for momentum, and the unit of each quantity?
What is the momentum of a stationary object?
What happens to momentum if the velocity doubles and the mass stays the same?
How do you rearrange $p = m v$ to find velocity?

5.7.1 Momentum

Momentum

Definition

Momentum

Momentum is the product of an object's mass and its velocity.

Every moving object has momentum because it has both mass and a velocity.
A stationary object has a velocity of $m/s0\ \text{m/s}$ , so its momentum is $m/s0\ \text{kg m/s}$ .
Momentum is a vector, so it has a size and a direction, pointing the same way as the velocity.
Momentum is calculated from $p = m v$ , where $p$ is momentum in $m/s\text{kg m/s}$ , $m$ is mass in $kg\text{kg}$ and $v$ is velocity in $m/s\text{m/s}$ .
For the same velocity, a greater mass gives greater momentum.
For the same mass, a greater velocity gives greater momentum.
If either the mass or the velocity doubles while the other stays the same, the momentum doubles.

Calculating momentum

To find momentum, put the mass in $kg\text{kg}$ and the velocity in $m/s\text{m/s}$ into $p = m v$ .
Convert grams to $kg\text{kg}$ and $km/h\text{km/h}$ to $m/s\text{m/s}$ before substituting.
You can rearrange $p = m v$ when the momentum is known: use $\dfrac{p}{v}$ to find mass, or $\dfrac{p}{m}$ to find velocity.

Example

A car of mass $kg1200\ \text{kg}$ travels at $m/s15\ \text{m/s}$ . Calculate its momentum.

State the equation: $p = m v$ .
Substitute the values: $\times 15$ .
Calculate the answer: $18\,000\ \text{kg m/s}$ .

Example

An object has momentum $m/s54\ \text{kg m/s}$ and mass $kg6.0\ \text{kg}$ . Calculate its velocity.

State the equation: $p = m v$ .
Rearrange for velocity: $\dfrac{p}{m}$ .
Substitute the values: $\dfrac{54}{6.0}$ .
Calculate the answer: $9.0\ \text{m/s}$ .

Common Mistake

Do not confuse momentum with force: momentum is measured in $m/s\text{kg m/s}$ , never in newtons.
Always use mass in $kg\text{kg}$ ; if it is given in grams, divide by $1000$ first.
Always use velocity in $m/s\text{m/s}$ , not $km/h\text{km/h}$ .

Exam technique

Write $p = m v$ before substituting, so you can still earn the equation mark if the arithmetic slips.
Show any rearrangement, substitute with units, and give the answer in $m/s\text{kg m/s}$ .

Self review

What is momentum?
What is the equation for momentum, and the unit of each quantity?
What is the momentum of a stationary object?
What happens to momentum if the velocity doubles and the mass stays the same?
How do you rearrange $p = m v$ to find velocity?

5.7.1 Momentum

Momentum

Calculating momentum

Review 5.7.1 Momentum is a property of moving objects by teaching Genie

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5.7.1 Momentum is a property of moving objects

5.7.1 Momentum

Momentum

Calculating momentum

Review 5.7.1 Momentum is a property of moving objects by teaching Genie

Recap your knowledge with an interactive lesson

Remember key concepts with flashcards

5.7.1 Momentum is a property of moving objects

5.7.1 Momentum

Momentum

Calculating momentum

Review 5.7.1 Momentum is a property of moving objects by teaching Genie

Recap your knowledge with an interactive lesson

Remember key concepts with flashcards

5.7.1 Momentum is a property of moving objects Revision Guide

5.7.1 Momentum is a property of moving objects

5.7.1 Momentum

Momentum

Calculating momentum

Review 5.7.1 Momentum is a property of moving objects by teaching Genie

Recap your knowledge with an interactive lesson

Remember key concepts with flashcards

5.7.1 Momentum is a property of moving objects Revision Guide