Statement and physical meaning of Newton’s third law

A law of interactions

Newton’s third law, also known as the principle of reciprocal actions, describes what happens when two objects interact. It states:

If a body A exerts a force on a body B, then B exerts a force on A of the same magnitude and in the same direction, but in the opposite sense.

In vector notation: F(A→B) = -F(B→A)

Two forces, two different objects

The most common misconception is to believe that these two forces cancel each other out. This is incorrect: they can never cancel each other out because they are not acting on the same object. F(A→B) acts on B, and F(B→A) acts on A. Two forces that cancel each other out must act on the same object; this is not the case here.

Practical example: pushing a wall

When you push a wall with your hand, you exert a force on the wall. In return, the wall exerts an equal and opposite force on your hand: this is why you feel pressure on your palm, even though the wall does not move.

Action	Reaction
Hand pushes the wall (towards the wall)	Wall pushes the hand (towards you)
Foot pushes the ground (backwards)	Ground pushes the foot (forwards): you move forwards
Rocket ejects gas (downwards)	Gas pushes the rocket (upwards)

Why it works

This law shows that an isolated force does not exist: a force is always the result of an interaction between two bodies. This is why we talk about an ‘action-reaction pair’ rather than two independent forces.