Newton's third law of motion

Newton's third law says that whenever two objects interact, the forces they exert on each other are equal in size and opposite in direction. If you push on a wall with a force of 50 N, the wall pushes back on you with 50 N. The two forces act on different objects, so they never cancel each other out. It is often stated as "every action has an equal and opposite reaction".

Newton's third law of motion

AQA's GCSE specification states it as: whenever two objects interact, the forces they exert on each other are equal and opposite. Forces always come in pairs. You cannot push something without it pushing back on you.

How to spot a Newton's third law pair

The two forces in a third law pair always:

• act on two different objects, one on each;
• are the same type of force: both gravitational, both contact, both magnetic and so on;
• are equal in size;
• act in opposite directions, along the same line.

A handy way to name them: "the force of A on B" and "the force of B on A". If you can swap the two letters to get the partner, you have a third law pair.

Newton's third law examples

• Walking: your foot pushes backwards on the ground, and the ground pushes forwards on your foot. That forward push is what moves you.
• Swimming: your hands push water backwards, and the water pushes you forwards.
• A rocket: the engine pushes exhaust gases out downwards, and the gases push the rocket upwards. It does not need air to push against.
• A gun recoiling: the gun pushes the bullet forwards, and the bullet pushes the gun backwards into your shoulder.
• An apple and the Earth: the Earth pulls the apple down with a gravitational force, and the apple pulls the Earth up with an equal gravitational force.

Example 1: equal forces, different accelerations

Two ice skaters, of masses 60 kg and 40 kg, push off each other. Each feels a force of 120 N. Find their accelerations.

The forces are equal, by Newton's third law. The accelerations are not, because the masses differ. Using Newton's second law, a = F ÷ m:

• 60 kg skater: 120 ÷ 60 = 2 m/s²
• 40 kg skater: 120 ÷ 40 = 3 m/s²

They move apart in opposite directions, and the lighter skater speeds up more. This is the same physics as conservation of momentum.

Example 2: why the Earth does not move towards the apple

A 0.1 kg apple falls from a tree. The Earth pulls it down with a force of 0.1 × 9.8 = 0.98 N, so the apple pulls the Earth up with 0.98 N too. With the Earth's mass of 5.97 × 10²⁴ kg, from NASA's fact sheet, the Earth's acceleration is 0.98 ÷ (5.97 × 10²⁴) ≈ 1.6 × 10⁻²⁵ m/s². The forces are equal, but the Earth's acceleration is far too small ever to notice.

Now try matching some pairs. Find the partner force, then press Mark to check it in the course.

The book on the table: a common trap

A book rests on a table. Two forces act on the book: its weight, pulling down, and the normal contact force from the table, pushing up. They are equal and opposite, so the book stays still. But they are not a third law pair:

• they both act on the same object, the book;
• they are different types of force, one gravitational and one contact.

They are balanced forces, which is Newton's first law. The real third law pairs are:

The quickest test: if both forces act on the same object, they cannot be a third law pair.

Why don't the forces cancel?

Forces only cancel when they act on the same object. A third law pair acts on two different objects, so each force affects only its own object. When a horse pulls a cart, the cart pulls back on the horse equally. The cart moves because the horse's pull on it is bigger than the friction on the cart. The horse moves because the ground pushes it forwards harder than the cart pulls it back. To decide whether something accelerates, add up only the forces acting on that one object.

Common mistakes

• Calling balanced forces a third law pair. Weight and the normal force on a resting object are balanced, but both act on the same object.
• Thinking the bigger object pushes harder. A lorry hitting a fly exerts exactly the same force on the fly as the fly exerts on the lorry. The effects differ because the masses differ.
• Thinking the pair cancels. The forces act on different objects, so they cannot cancel.
• Naming different types of force. A third law pair is always the same type: gravity with gravity, contact with contact.

Newton's three laws together

• First law: if the resultant force on an object is zero, it stays at rest or keeps moving at a constant velocity.
• Second law: a resultant force causes an acceleration, F = ma.
• Third law: forces between two objects come in equal and opposite pairs.

The first two are about the forces on one object. The third is about the forces between two objects. The Laws of Motion course covers all three, with a section where you match each force to its partner.

Practise forces in a short timed paper

GCSE Physics Higher and A-level Physics: Year 1 each give you a short timed paper every day, with 8 questions worth 25 to 35 marks across the course.

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