It's written that the "bigger the change in momentum, the more force you need to apply to get that change in momentum," but couldn't the time the force is acting for be decreased too to make a bigger change in momentum?

Yes! If you use a certain net force and time to obtain impulse, then if you increase the net force and proportionately decrease the time or vice versa, you will obtain the same impulse (change in momentum).

Main content

Course: High school physics > Unit 6

Lesson 1: Introduction to linear momentum and impulse

Linear momentum review

Google Classroom

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 $\frac{kg \cdot m}{s}$ ‍.

Equations

Equation	Symbols	Meaning in words
$p = m v$ ‍	$p$ ‍ is momentum, $m$ ‍ is mass, and $v$ ‍ is velocity	Momentum is mass times velocity.
$Δ p = F_{net} Δ t$ ‍	$F_{net}$ ‍ is the net external force, $Δ p$ ‍ is change in momentum, and $Δ t$ ‍ is the time over which a net force acts	Change 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

Δ v

can also be written as

a Δ t

. We can then see that any change in momentum following an acceleration can be written as

\begin{aligned} Δ p & = m Δ v \\ = m (a Δ t) \\ = F_{net} Δ t \end{aligned}

If we rearrange this to solve for

F_{net}

when the mass of the system and net force is constant, we get Newton’s second law

F_{net} = \frac{Δ p}{Δ 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

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.

Learn more

For deeper explanations of linear momentum, see our introduction to momentum video.

To check your understanding and work toward mastering these concepts, check out our linear momentum exercises:

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Anya Chan
Posted 4 years ago. Direct link to Anya Chan's post “It's written that the "bi...”
It's written that the "bigger the change in momentum, the more force you need to apply to get that change in momentum," but couldn't the time the force is acting for be decreased too to make a bigger change in momentum?
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(6 votes)
Answer
- arijwei
  Posted 4 years ago. Direct link to arijwei's post “Yes! If you use a certain...”
  Yes! If you use a certain net force and time to obtain impulse, then if you increase the net force and proportionately decrease the time or vice versa, you will obtain the same impulse (change in momentum).
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  (5 votes)
Vivienne Raczkowski
Posted 4 years ago. Direct link to Vivienne Raczkowski's post “In a question where momen...”
In a question where momentum is in (kg x m)/s,
and the value for time is in ms, would you need to convert ms to seconds for your final answer?
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(2 votes)
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- obiwan kenobi
  Posted 4 years ago. Direct link to obiwan kenobi's post “Yes, you would. Otherwise...”
  Yes, you would. Otherwise your answer would have the units (kg * m)/ms. If you want the units to be (kg * m)/s, you have to convert from ms to s.
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  (1 vote)
127394
Posted 4 years ago. Direct link to 127394's post “How is it you have to sol...”
How is it you have to solve for this in any other way
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(2 votes)
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Gabe Smith
Posted a year ago. Direct link to Gabe Smith's post “whats the difference betw...”
whats the difference between momentum and kinetic energy
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(2 votes)
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- Sukhada
  Posted 8 months ago. Direct link to Sukhada's post “They are both related to ...”
  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.
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  (1 vote)
tcastellano
Posted 3 years ago. Direct link to tcastellano's post “Is there any version of t...”
Is there any version of these articles that are printer friendly. I would like to have these for my students to follow along, but I cannot figure out a way to print them nicely. Any recommendations?
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(1 vote)
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Morgan Fude
Posted 4 months ago. Direct link to Morgan Fude's post “when finding the magnitud...”
when finding the magnitude of the net force why is the time multiplied by 10 to the -3 seconds?
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(1 vote)
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- big sigma bumboclatt
  Posted a month ago. Direct link to big sigma bumboclatt's post “big bumboclatt”
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