A book rests on a table. What is the partner of the force the table exerts on the book?

The given force: table on book, upwards. Swap the bodies and reverse the direction. The force the book exerts on the table, downwards. Not its weight

Why are the book's weight and the normal force not an action-reaction pair?

Both act on the same body — the book. An action-reaction pair acts on two different bodies. They balance only because the book is at rest. They are two forces balancing on one body, which is something else entirely

A rocket expels gas backwards. What accelerates it?

The rocket exerts a backward force on the gas. The gas exerts an equal forward force on the rocket. The gas itself. No external air is needed

Newton's Laws · Grade 11

If every force has an equal and opposite partner, how does anything move?

Because the two forces act on different bodies. The force I exert on the wall acts on the wall, and the force the wall exerts on me acts on me. Forces only cancel when they act on the same body, which is why an action-reaction pair never cancels out.

Learning objectives

Name the partner of a given force and say which body that partner acts on
Explain how a horse can pull a cart forward even though the cart pulls back on it with an equal force
Explain how a rocket accelerates in space with nothing outside it to push against
Tell an action and reaction pair apart from two forces that balance on the same body

The condition everything hangs on

When body A exerts a force on body B, body B exerts an equal and opposite force on body A. Always, instantly, without exception.

The important word is 'on'. The first force acts on B and the second on A. Two forces acting on different bodies cannot cancel, because cancelling is something that happens within one diagram.

A quick test for naming the partner: reverse the order. 'The Earth pulls the apple' becomes 'the apple pulls the Earth'. Same size, opposite direction, bodies swapped.

The horse and the cart

If the cart pulls the horse with the same force the horse pulls the cart, how does the pair move at all? The puzzle dissolves the moment you separate the diagrams.

On the cart: the horse's pull forward, and ground friction backward. If the pull exceeds the friction, the cart accelerates. The cart's pull on the horse does not appear in this diagram at all.

On the horse: the cart's pull backward, and above all the ground's friction forward on its hooves. That is the force that drives the horse — the ground, not the cart. Which is why a horse on ice gets nowhere, though it pulls with exactly the same force.

A rocket in space

It is common to think a rocket pushes against the air. If that were true it would not work in space, and it works better there.

The rocket pushes gas backwards at high speed. By the third law the gas pushes the rocket forwards with the same force. That is the entire mechanism, and it needs nothing external to push against.

The same idea explains swimming, walking and rowing: push water, ground or air one way, and it pushes you the other.

Worked examples

A book rests on a table. What is the partner of the force the table exerts on the book?
1. The given force: table on book, upwards
2. Swap the bodies and reverse the direction
Answer: The force the book exerts on the table, downwards. Not its weight
Why are the book's weight and the normal force not an action-reaction pair?
1. Both act on the same body — the book
2. An action-reaction pair acts on two different bodies
3. They balance only because the book is at rest
Answer: They are two forces balancing on one body, which is something else entirely
A rocket expels gas backwards. What accelerates it?
1. The rocket exerts a backward force on the gas
2. The gas exerts an equal forward force on the rocket
Answer: The gas itself. No external air is needed

Common mistakes

Cancelling an action-reaction pair against each other: They act on different bodies and so cannot cancel. Cancelling happens only within one body's diagram.
Naming the book's weight as the partner of the normal force: Both act on the book. The partner of its weight is the book's pull on the Earth, and the partner of the normal force is the book's push on the table.
Thinking the stronger one wins the pair: In an action-reaction pair the magnitudes are always equal. Whichever accelerates more is the one with the smaller mass, not the larger force.

What to remember

Action and reaction: equal, opposite, on different bodies.
Which is why they never cancel.
The ground drives the horse, not the cart.
A rocket is pushed by its own exhaust.