Inertia

Definition

Inertia

A measure of how difficult it is to change the velocity of an object.

Inertia is a measure of how difficult it is to change the velocity of an object.
A change in velocity includes starting to move, speeding up, slowing down, stopping and changing direction.
Every object has inertia, whether it is moving or at rest.
1. A stationary object resists being set in motion.
2. A moving object resists being slowed down, stopped or turned.
The greater the mass of an object, the greater its inertia, so the harder it is to change its velocity.
An empty supermarket trolley is easy to start, stop and steer, while a fully loaded trolley needs a much bigger push to do the same things.
A loaded lorry needs a much larger braking force than a small car to stop in the same distance, because it has far more inertia.
Inertia explains why passengers on a bus lurch forwards when it brakes suddenly, because their bodies keep moving forwards until a force from the seat belt or the seat in front changes their velocity.
Inertia is a property of the object, not a force, so it is never drawn on a free body diagram.

Inertial mass

Definition

Inertial mass

The ratio of the resultant force acting on an object to the acceleration that the force produces.

The inertial mass of an object puts a number on its inertia.
Inertial mass is defined as the ratio of the resultant force to the acceleration it produces.
In words, $forceacceleration\text{inertial mass}=\dfrac{\text{resultant force}}{\text{acceleration}}$ .
In symbols, $m=Fam=\dfrac{F}{a}$ , where $m$ is in $kg\text{kg}$ , $F$ is in $N\text{N}$ and $a$ is in $m/s2\text{m/s}^2$ .
An object with a large inertial mass gains only a small acceleration from a given resultant force.
1. A resultant force of $N600\ \text{N}$ gives a $kg60\ \text{kg}$ sprinter an acceleration of $m/s210\ \text{m/s}^2$ .
2. The same $N600\ \text{N}$ gives a $kg1200\ \text{kg}$ car an acceleration of only $m/s20.5\ \text{m/s}^2$ .
Measuring the force on an object and its acceleration is one way to find its mass without using a balance.
This method works in places where a balance would be useless, such as on board the International Space Station, where objects appear weightless but still have inertia.
1. Astronauts find their mass by measuring how quickly a known force accelerates them.
The force in the equation must be the resultant force, so opposing forces are combined before you divide by the acceleration.

Example

Inertial mass of a car

A resultant force of $N3600\ \text{N}$ gives a car an acceleration of $m/s22.4\ \text{m/s}^2$ .

m=\dfrac{F}{a}

m=\dfrac{3600\ \text{N}}{2.4\ \text{m/s}^2}=1500\ \text{kg}

The inertial mass of the car is $kg1500\ \text{kg}$ .

Example

Comparing the inertia of two trolleys

The same resultant force of $N12\ \text{N}$ acts in turn on two trolleys, A and B.
Trolley A accelerates at $m/s23.0\ \text{m/s}^2$ and trolley B accelerates at $m/s21.5\ \text{m/s}^2$ .

m_{\text{A}}=\dfrac{12\ \text{N}}{3.0\ \text{m/s}^2}=4.0\ \text{kg}

m_{\text{B}}=\dfrac{12\ \text{N}}{1.5\ \text{m/s}^2}=8.0\ \text{kg}

Trolley B has twice the inertial mass of trolley A, so it has the greater inertia and its velocity is harder to change.

Common Mistake

Do not call inertia a force, because it is a property that describes how hard it is to change an object's velocity.
Do not say that inertia only affects moving objects, because a stationary object also resists being made to move.
Do not use a single force in $m=Fam=\dfrac{F}{a}$ when other forces act, because inertial mass is defined using the resultant force.

Exam technique

Defining inertia and inertial mass

For inertia, write "a measure of how difficult it is to change the velocity of an object", using the word velocity rather than "movement".
For inertial mass, write that it is "the ratio of resultant force to acceleration", and give the equation $m=Fam=\dfrac{F}{a}$ .
In a comparison, link a larger mass to a smaller acceleration for the same resultant force.

Self review

What is inertia?
How is inertial mass defined?
Explain why a loaded lorry is harder to stop than a small car.
Calculate the inertial mass of an object that accelerates at $m/s24.0\ \text{m/s}^2$ when the resultant force on it is $N20\ \text{N}$ .
Why can a balance not be used to find the mass of an astronaut on the International Space Station?

Inertia

Definition

Inertia

A measure of how difficult it is to change the velocity of an object.

Inertia is a measure of how difficult it is to change the velocity of an object.
A change in velocity includes starting to move, speeding up, slowing down, stopping and changing direction.
Every object has inertia, whether it is moving or at rest.
1. A stationary object resists being set in motion.
2. A moving object resists being slowed down, stopped or turned.
The greater the mass of an object, the greater its inertia, so the harder it is to change its velocity.
An empty supermarket trolley is easy to start, stop and steer, while a fully loaded trolley needs a much bigger push to do the same things.
A loaded lorry needs a much larger braking force than a small car to stop in the same distance, because it has far more inertia.
Inertia explains why passengers on a bus lurch forwards when it brakes suddenly, because their bodies keep moving forwards until a force from the seat belt or the seat in front changes their velocity.
Inertia is a property of the object, not a force, so it is never drawn on a free body diagram.

Inertial mass

Definition

Inertial mass

The ratio of the resultant force acting on an object to the acceleration that the force produces.

The inertial mass of an object puts a number on its inertia.
Inertial mass is defined as the ratio of the resultant force to the acceleration it produces.
In words, $forceacceleration\text{inertial mass}=\dfrac{\text{resultant force}}{\text{acceleration}}$ .
In symbols, $m=Fam=\dfrac{F}{a}$ , where $m$ is in $kg\text{kg}$ , $F$ is in $N\text{N}$ and $a$ is in $m/s2\text{m/s}^2$ .
An object with a large inertial mass gains only a small acceleration from a given resultant force.
1. A resultant force of $N600\ \text{N}$ gives a $kg60\ \text{kg}$ sprinter an acceleration of $m/s210\ \text{m/s}^2$ .
2. The same $N600\ \text{N}$ gives a $kg1200\ \text{kg}$ car an acceleration of only $m/s20.5\ \text{m/s}^2$ .
Measuring the force on an object and its acceleration is one way to find its mass without using a balance.
This method works in places where a balance would be useless, such as on board the International Space Station, where objects appear weightless but still have inertia.
1. Astronauts find their mass by measuring how quickly a known force accelerates them.
The force in the equation must be the resultant force, so opposing forces are combined before you divide by the acceleration.

Example

Inertial mass of a car

A resultant force of $N3600\ \text{N}$ gives a car an acceleration of $m/s22.4\ \text{m/s}^2$ .

m=\dfrac{F}{a}

m=\dfrac{3600\ \text{N}}{2.4\ \text{m/s}^2}=1500\ \text{kg}

The inertial mass of the car is $kg1500\ \text{kg}$ .

Example

Comparing the inertia of two trolleys

The same resultant force of $N12\ \text{N}$ acts in turn on two trolleys, A and B.
Trolley A accelerates at $m/s23.0\ \text{m/s}^2$ and trolley B accelerates at $m/s21.5\ \text{m/s}^2$ .

m_{\text{A}}=\dfrac{12\ \text{N}}{3.0\ \text{m/s}^2}=4.0\ \text{kg}

m_{\text{B}}=\dfrac{12\ \text{N}}{1.5\ \text{m/s}^2}=8.0\ \text{kg}

Trolley B has twice the inertial mass of trolley A, so it has the greater inertia and its velocity is harder to change.

Common Mistake

Do not call inertia a force, because it is a property that describes how hard it is to change an object's velocity.
Do not say that inertia only affects moving objects, because a stationary object also resists being made to move.
Do not use a single force in $m=Fam=\dfrac{F}{a}$ when other forces act, because inertial mass is defined using the resultant force.

Exam technique

Defining inertia and inertial mass

For inertia, write "a measure of how difficult it is to change the velocity of an object", using the word velocity rather than "movement".
For inertial mass, write that it is "the ratio of resultant force to acceleration", and give the equation $m=Fam=\dfrac{F}{a}$ .
In a comparison, link a larger mass to a smaller acceleration for the same resultant force.

Self review

What is inertia?
How is inertial mass defined?
Explain why a loaded lorry is harder to stop than a small car.
Calculate the inertial mass of an object that accelerates at $m/s24.0\ \text{m/s}^2$ when the resultant force on it is $N20\ \text{N}$ .
Why can a balance not be used to find the mass of an astronaut on the International Space Station?

2.2.10 Inertia and inertial mass

Inertia

Inertial mass

Inertial mass of a car

Comparing the inertia of two trolleys

Defining inertia and inertial mass

Review 2.2.10 Inertia and inertial mass by teaching Genie

2.2.10 Inertia and inertial mass

Inertia

Inertial mass

Inertial mass of a car

Comparing the inertia of two trolleys

Defining inertia and inertial mass

Review 2.2.10 Inertia and inertial mass by teaching Genie

2.2.10 Inertia and inertial mass

Inertia

Inertial mass

Inertial mass of a car

Comparing the inertia of two trolleys

Defining inertia and inertial mass

Review 2.2.10 Inertia and inertial mass by teaching Genie

2.2.10 Inertia and inertial mass Revision Guide

2.2.10 Inertia and inertial mass

Inertia

Inertial mass

Inertial mass of a car

Comparing the inertia of two trolleys

Defining inertia and inertial mass

Review 2.2.10 Inertia and inertial mass by teaching Genie

2.2.10 Inertia and inertial mass Revision Guide