Newton's Third Law of Motion

The Mutual Nature of Force

The second law tells us how a force changes a body's motion, but it leaves a deeper question unanswered: where does that external force come from? Newtonian mechanics gives a simple, consistent answer — every external force on a body originates from some other body. Forces are never solitary; they are always an interaction between two bodies.

Consider two bodies, A and B. If B exerts a force on A, does A exert a force back on B? In some cases the answer is obvious. Press a coiled spring with your hand — the spring compresses under the force from your hand, and the compressed spring pushes back against your hand. You feel that push directly. But what about non-contact forces? The Earth pulls a stone downward due to gravity. Does the stone pull back on the Earth? The effect is not obvious because the Earth is so massive that the stone's pull produces negligible acceleration. Newton's answer was clear: yes, the stone exerts an equal and opposite force on the Earth. We simply do not notice it.

This insight — that force is mutual, that forces always occur in pairs, and that the mutual forces between two bodies are always equal and opposite — is the essence of Newton's third law of motion.

The wording is so crisp that it has entered common language, but that very familiarity breeds misconceptions. Let us examine three critical points that clarify what the law actually means.

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Point 1: Action and Reaction Are Just Forces

The words "action" and "reaction" in the third law mean nothing other than "force." Using different names for the same physical concept can cause confusion. A clearer, more modern statement is:

Forces always occur in pairs. The force on body A due to body B is equal and opposite to the force on body B due to body A.

If we denote the force on A by B as $\mathbf{F}_{AB}$, and the force on B by A as $\mathbf{F}_{BA}$, the third law states:

The minus sign indicates that the two forces act in opposite directions.

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Point 2: No Cause-Effect Relationship

The words "action" and "reaction" might suggest that action comes first — that action is the cause and reaction the effect. This is wrong. The two forces exist simultaneously. There is no time delay between them. Either force can be called the action and the other the reaction; the naming is arbitrary.

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Point 3: Action and Reaction Act on Different Bodies

This is the most important point and the most common source of error. The two forces in a third-law pair act on different bodies. Consider bodies A and B again:

• $\mathbf{F}_{AB}$ acts on A (due to B).
• $\mathbf{F}_{BA}$ acts on B (due to A). …