IB Physics Topic A.2.2 Linear Momentum and Impulse Revision Notes (SL/HL)

IB Physics Topic A.2.2 Linear Momentum and Impulse Revision Notes (SL/HL) | RevisionDojo

Written by official IB examiners

What is Momentum?

Definition

Momentum

Momentum is a measure of how difficult it is to stop a moving object. It depends on two factors: the object's mass and its velocity.

Momentum is defined as the product of an object's mass and its velocity:

$$
\vec{p} = m \vec{v}
$$

where $\vec{p}$ is the momentum (in $\text{kg m s}^{-1}$), $m$ is the mass (in $\text{kg}$), $\vec{v}$ is the velocity (in $\text{m s}^{-1}$).

Newton originally expressed his Second Law in terms of momentum rather than acceleration.

He stated that:

"The rate of change of momentum of an object is proportional to the force applied, and takes place in the direction of the force."

This can be written as:

$$
\vec{F} = \frac{\Delta\vec{p}}{\Delta t}
$$

Example

This form is particularly useful when dealing with systems where the mass is not constant, such as a rocket.
As a rocket burns fuel, it ejects mass backward and becomes lighter over time.
Even though the total system’s mass is changing, the force generated by the rocket engines can still be understood as the rate of change of momentum.
For example, if a rocket expels gas backward at high velocity, the momentum of the expelled gas increases in one direction, and by conservation of momentum, the rocket gains momentum in the opposite direction.
This causes the rocket to accelerate.

For systems with changing mass, such as a rocket, the simple form $\vec{F} = m \vec{a}$ is not sufficient.
Instead, we rely on: $$\vec{F} = \frac{\Delta \vec{p}}{\Delta t}$$
It could be written more rigorously for a system as: $$\vec{F}_{\text{ext}} = \frac{d\vec{p}_{\text{system}}}{dt}$$ which makes clear that the net external force equals the time rate of change of the system’s total momentum.
When the mass is constant, this equation simplifies to the more familiar form: $$\vec{F} = m \frac{d\vec{v}}{dt} = m \vec{a}$$

Momentum is Conserved in Isolated Systems

Momentum helps us understand how objects behave during interactions like collisions or explosions.

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What is Momentum?

Definition

Momentum

Momentum is a measure of how difficult it is to stop a moving object. It depends on two factors: the object's mass and its velocity.

Momentum is defined as the product of an object's mass and its velocity:

$$
\vec{p} = m \vec{v}
$$

where $\vec{p}$ is the momentum (in $\text{kg m s}^{-1}$), $m$ is the mass (in $\text{kg}$), $\vec{v}$ is the velocity (in $\text{m s}^{-1}$).

Newton originally expressed his Second Law in terms of momentum rather than acceleration.

He stated that:

"The rate of change of momentum of an object is proportional to the force applied, and takes place in the direction of the force."

This can be written as:

$$
\vec{F} = \frac{\Delta\vec{p}}{\Delta t}
$$

Example

This form is particularly useful when dealing with systems where the mass is not constant, such as a rocket.
As a rocket burns fuel, it ejects mass backward and becomes lighter over time.
Even though the total system’s mass is changing, the force generated by the rocket engines can still be understood as the rate of change of momentum.
For example, if a rocket expels gas backward at high velocity, the momentum of the expelled gas increases in one direction, and by conservation of momentum, the rocket gains momentum in the opposite direction.
This causes the rocket to accelerate.

For systems with changing mass, such as a rocket, the simple form $\vec{F} = m \vec{a}$ is not sufficient.
Instead, we rely on: $$\vec{F} = \frac{\Delta \vec{p}}{\Delta t}$$
It could be written more rigorously for a system as: $$\vec{F}_{\text{ext}} = \frac{d\vec{p}_{\text{system}}}{dt}$$ which makes clear that the net external force equals the time rate of change of the system’s total momentum.
When the mass is constant, this equation simplifies to the more familiar form: $$\vec{F} = m \frac{d\vec{v}}{dt} = m \vec{a}$$

Momentum is Conserved in Isolated Systems

Momentum helps us understand how objects behave during interactions like collisions or explosions.

Definition

Paywall

(on a website) an arrangement whereby access is restricted to users who have paid to subscribe to the site.

anim nostrud sit dolore minim proident quis fugiat velit et eiusmod nulla quis nulla mollit dolor sunt culpa aliqua

Duis aute irure dolor in reprehenderit

Note

Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam quis nostrud exercitation.

Excepteur sint occaecat cupidatat non proident

Tip

Lorem ipsum dolor sit amet, consectetur adipiscing elit.
Sed do eiusmod tempor incididunt ut labore et dolore magna aliqua.
Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris.
Duis aute irure dolor in reprehenderit in voluptate velit esse cillum.

Topic A - Space, time and motion5 subtopics

Topic B - The particulate nature of matter5 subtopics

Topic C - Wave behaviour5 subtopics

Topic D - Fields4 subtopics

Topic E - Nuclear and quantum physics5 subtopics

IB Physics A.2.2 Linear Momentum and Impulse Notes

Topic A - Space, time and motion5 subtopics

Topic B - The particulate nature of matter5 subtopics

Topic C - Wave behaviour5 subtopics

Topic D - Fields4 subtopics

Topic E - Nuclear and quantum physics5 subtopics

What is Momentum?

Momentum is Conserved in Isolated Systems

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Duis aute irure dolor in reprehenderit

Excepteur sint occaecat cupidatat non proident

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What is Momentum?

Momentum is Conserved in Isolated Systems

anim nostrud sit dolore minim proident quis fugiat velit et eiusmod nulla quis nulla mollit dolor sunt culpa aliqua

Duis aute irure dolor in reprehenderit

Excepteur sint occaecat cupidatat non proident

Unlock the rest of this chapter with a free account