GCSE · Physics · Edexcel · Spec 1PH0

Inertial mass

Shove an empty shopping trolley and it shoots off. Give a loaded one the same shove and it barely gets going. Once rolling, it's just as hard to stop.

Higher

Same acceleration — how much force?

Inertial mass 2 kg

Inertial mass: 2 kg. Force needed for 2 m/s²: 4 N

Each line is one object. Lift the point and you are asking for the same 2 m/s² — the same change of velocity every second — from an object with more inertial mass. It takes more force, so the line gets steeper. Now read any point on one line — at the starting 2 kg, 2 N ÷ 1 m/s², 4 N ÷ 2 m/s² and 8 N ÷ 4 m/s² all give 2. Force ÷ acceleration is the same everywhere on the line, and that number is the inertial mass.

Watch out: A steeper line here does not mean a bigger acceleration. It is steeper because every extra 1 m/s² costs more newtons — which is exactly what a larger inertial mass means.

Higher

Does mass only matter when you're starting off?

An empty trolley and a fully loaded trolley are rolling across a car park side by side, at the same velocity. You need to stop each one, or steer it round a corner.

Which is closest to what you think right now?

Mass only matters for getting it moving. Once they're both rolling, the loaded one is just as easy to stop or steer.The loaded one is harder to start, harder to stop and harder to steer. Any change to its velocity takes more force.Once it's moving, the loaded one keeps going because its mass pushes it forward.Steering round a corner at a steady speed isn't a change of velocity, so mass makes no difference there.

How sure are you?

I'm sureI think soI'm guessing

Mass only matters for getting it moving. Once they're both rolling, the loaded one is just as easy to stop or steer.

This is a common misconception

Starting from rest is only one kind of velocity change. Stopping changes the velocity too (all the way down to zero), and so does steering, because velocity has a direction. The loaded trolley resists every one of those changes more: for the same force it slows down less, and its direction changes less.

The loaded one is harder to start, harder to stop and harder to steer. Any change to its velocity takes more force.

This matches the evidence

Spot on. Inertial mass measures how difficult it is to change velocity in any way: from rest, speeding up, slowing down, stopping or changing direction. Bigger inertial mass, smaller acceleration from the same resultant force.

Once it's moving, the loaded one keeps going because its mass pushes it forward.

This is a common misconception

Mass isn't a push. Inertial mass is a property of the trolley itself — how much it resists a change in velocity. Forces from outside are what change the velocity; inertial mass decides how big a change a given force can make.

Steering round a corner at a steady speed isn't a change of velocity, so mass makes no difference there.

This is a common misconception

Velocity is speed in a particular direction. Change the direction and you have changed the velocity, even if the speed never changes. So steering needs a resultant force too, and the loaded trolley needs a bigger one to turn the same way.

Inertial mass is about ANY change of velocity — starting, speeding up, slowing down, stopping or turning. More inertial mass means more resistance to all of them.

Higher

Putting a number on it

Problem

A resultant force of 120 N acts on a loaded trolley, and it accelerates at 2.5 m/s². (a) What is its inertial mass? (b) The same 120 N then acts on an empty trolley with an inertial mass of 12 kg. How do the two accelerations compare?

Higher

Don't judge by the force alone

Rank the objects by inertial mass — how difficult it is to change each one's velocity

1 · Easiest to change (smallest inertial mass)4 · Hardest to change (largest inertial mass)

Object C: a 90 N resultant force gives it 9 m/s²
Object D: a 12 N resultant force gives it 0.5 m/s²
Object A: a 20 N resultant force gives it 4 m/s²
Object B: a 60 N resultant force gives it 3 m/s²

WHAT YOU'VE LEARNED

A quick recap of today's lesson.

Why is a loaded trolley so hard to get going — and so hard to stop?

What you need to know

Inertial mass is a measure of how difficult it is to change an object's velocity — including getting it moving from rest.
Changing velocity means speeding up, slowing down, stopping or changing direction.
Inertial mass is defined as the ratio of force over acceleration: inertial mass = resultant force ÷ acceleration.
Units: resultant force in newtons (N), acceleration in metres per second squared (m/s²), inertial mass in kilograms (kg).

The big picture

Inertial mass is a measure of how difficult it is to change an object's velocity — to get it moving from rest, speed it up, slow it down, stop it or turn it. The bigger the inertial mass, the smaller the acceleration a given resultant force produces. Inertial mass is defined as the ratio of force over acceleration: inertial mass = resultant force ÷ acceleration, measured in kilograms.

Key points

1Same resultant force, bigger inertial mass → smaller acceleration.

2On a graph of resultant force against acceleration, one object gives a straight line through the origin, and its gradient is its inertial mass.

3To compare objects, work out force ÷ acceleration for each; the size of the force alone tells you nothing.

4Inertial mass is a property of the object, not a force acting on it.

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Worked example

Problem

A shopping trolley with an inertial mass of 40 kg is rolling along. You want to slow it down at 1.5 m/s². What resultant force do you need?

⚠ Watch out

Writing the ratio upside down, as acceleration ÷ force. Inertial mass is force ÷ acceleration. Quick check: an object that needs a bigger force for the same acceleration must have a bigger inertial mass, so force goes on top.

🧠

Memory hook

Force on top, acceleration underneath. Inertial mass is the number of newtons it costs to buy each 1 m/s² of acceleration.

✓

Check yourself

A resultant force of 36 N gives a sledge an acceleration of 1.2 m/s². What is its inertial mass? (Answer: 36 ÷ 1.2 = 30 kg.)

Flashcards

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What is inertial mass?

A measure of how difficult it is to change an object's velocity (including getting it moving from rest).

How is inertial mass defined as a ratio?

Inertial mass = resultant force ÷ acceleration.

The same resultant force acts on two objects. Which one accelerates less?

The one with the larger inertial mass.

Name the ways an object's velocity can change.

Speeding up (including from rest), slowing down, stopping, or changing direction.

Graph of resultant force (y) against acceleration (x) for one object: what is the gradient?

Its inertial mass — force ÷ acceleration has the same value at every point on the line.

Newtons ÷ metres per second squared gives which unit?

Kilograms (kg), the unit of inertial mass.

Is inertial mass a force?

No. It is a property of the object — how much it resists a change in velocity. Forces are what change the velocity.

Tap any card to flip it, or use Study as deck to go through them one at a time. In the full lesson these run as a spaced-repetition deck — you rate each card Hard, Good or Easy and the tricky ones keep coming back until they stick.

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Same acceleration — how much force?

Does mass only matter when you're starting off?

Don't judge by the force alone

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