Newton's Third Law

Newton’s third law states that whenever two objects interact, the forces they exert on each other are equal in magnitude and opposite in direction. These forces are called a third-law pair, sometimes described as an action–reaction pair. They occur together: the word ‘reaction’ does not mean that one force happens later.

Each force acts on a different object. For example, when your foot pushes the ground backwards, the ground pushes your foot forwards with an equally large force. The forward force from the ground helps you move forwards.

Identifying the two forces

To identify a third-law pair, first name the two interacting objects. Then describe the force in each direction: A exerts a force on B, and B exerts a force on A.

The forces must be:

• equal in magnitude;
• opposite in direction;
• acting on different objects;
• the same type of force, because they belong to the same interaction.

For example, the Earth pulls a book downwards by gravity, and the book pulls the Earth upwards by gravity. Both forces are gravitational. Neither is the contact force exerted by a table.

Force arrows represent direction by the way they point and magnitude by their length. Equal-length arrows pointing in opposite directions can represent a third-law pair, but only if their labels show that they act on different objects.

A book at rest: equilibrium is not a third-law pair

Consider a book resting on a horizontal table. Two forces act on the book: its weight acts downwards, and the table’s normal contact force acts upwards. They are equal in magnitude, so the resultant force—the overall force on the book—is zero. The book is in equilibrium and remains at rest.

These two forces are not a third-law pair. They both act on the book, and they arise from different interactions: gravity and contact.

The actual third-law pairs are:

• Contact pair: the table pushes upwards on the book; the book pushes downwards on the table.
• Gravitational pair: the Earth pulls downwards on the book; the book pulls upwards on the Earth.

A diagram showing only the forces acting on the book is a free-body diagram. It is useful for deciding whether the book’s forces are balanced, but it cannot show both members of a third-law pair: the partner force acts on another object.

A collision: equal forces can still change motion

Newton’s third law also applies in non-equilibrium situations. Imagine trolley A moving to the right and colliding with stationary trolley B. During contact, A pushes B to the right, while B pushes A to the left with an equally large force.

If these contact forces are not balanced by other horizontal forces, B speeds up to the right and A slows down. The forces do not cancel on either trolley: one acts on A and the other acts on B.

Equal interaction forces do not necessarily produce equal accelerations. For the same resultant force, a smaller mass has a larger acceleration. The trolleys can therefore respond differently even though the forces they exert on each other are equal.

The distinction is the same in both examples: Newton’s third law compares forces on two different objects; equilibrium depends on the resultant force on one object.