Edexcel IGCSE Physics · Spec 1.11
Momentum & Newton's Third Law
Momentum and Newton's third law of motion.
Physics revision video
Momentum & Newton's Third Law
Prefer to watch on YouTube? Open this video on YouTube.
Explained
Momentum, and the law that explains why it is conserved
Momentum is mass multiplied by velocity, and because velocity has a direction, so does momentum. Two objects of the same mass moving at the same speed in opposite directions have equal and opposite momenta, and together they have none.
Newton's third law and conservation of momentum are usually taught as two separate facts. They are not. One is the reason for the other, and seeing that connection makes both easier to state correctly.
Stating the third law properly
When object A exerts a force on object B, object B exerts a force on object A that is equal in size and opposite in direction.
The old wording, that every action has an equal and opposite reaction, is accepted, but it leaves out the part that questions test. The two forces act on different objects. That is the whole content of the law, and it is the clause most often missing.
If both forces acted on the same object they would cancel and nothing could ever accelerate. A book on a table pushes down on the table and the table pushes up on the book; those are the third law pair, acting on two different things. The weight of the book and the upward push of the table both act on the book, so they are not a third law pair at all, even though they happen to be equal here.
Why that gives conservation of momentum
In a collision the two objects push on each other for exactly the same length of time, and by the third law with equal and opposite forces.
Force multiplied by time gives change in momentum. So each object experiences the same size of momentum change, in opposite directions. One gains exactly what the other loses, and the total is unchanged.
That is why conservation of momentum needs no external force to be acting. An outside force would add momentum to the system without taking any away from anywhere inside it.
The examples worth knowing
A rifle recoils because it pushes the bullet forward and the bullet pushes the rifle back with an equal force. The bullet is far lighter, so it gains far more speed for the same momentum.
A rocket pushes exhaust gases backwards, so the gases push the rocket forwards. This works in space, because the rocket is pushing on its own exhaust rather than on the air.
Swimming, walking and rowing are all the same idea. You push the water, the ground or the oar backwards, and it pushes you forwards.
What examiners say about this topic
A principal examiner report for Edexcel International GCSE Physics describes a collision question where the majority of candidates scored highly, then adds one sentence that is worth more than the rest: some candidates mistook moment, energy or force for momentum.
Moment and momentum differ by two letters and belong to different topics. A moment is a turning effect, measured in newton metres. Momentum is mass times velocity, measured in kilograms metres per second. An examiner reading moment has to mark moment.
On the last part of that question, the report says it required knowledge of Newton's third law, so that the magnitude of the force was the same as the candidate's previous answer and to the right, so that it decelerated the second object.
That is the third law used as a calculation shortcut rather than as a sentence to recite. The force on the second object did not have to be worked out at all, because it has to equal the force on the first one. The only thing left to decide was the direction, and the report shows the direction being justified by what it does to the object rather than asserted.
The corresponding mark scheme splits that part into two marks: the magnitude, taken from the candidate's own earlier answer, and the direction. So a candidate who made an arithmetic slip earlier still collects both marks here, provided the reasoning is right.
Answering a third law question
Name both objects, and say which pushes which.
A complete answer has three parts: the first object exerts a force on the second, the second exerts an equal force back on the first, and that force is in the opposite direction. Naming the objects is what separates an answer that has understood the law from one that has memorised a slogan.
Where a question gives you one force in a pair and asks for the other, the size is already decided. Only the direction, and which object it acts on, remain to be said.
Spec 1.11
What you need to know
- Define momentum
- State conservation of momentum
- State Newton's third law
Active recall
Quick check
Answer each question before opening the answer.
What is the equation for momentum?
Momentum = mass × velocity (p = m × v).
State Newton's third law of motion.
For every action there is an equal and opposite reaction.
Physics revision app
Take this topic further in the app
275 guided topics with questions marked as you answer them, section checkpoints and timed practice papers. Fifteen topics are free to try, with no card needed.