Newton's Third Law — Action and Reaction

Newton's Third Law is the most frequently misquoted and misunderstood of the three. Generations of students repeat the mantra "every action has an equal and opposite reaction" without ever being taught the crucial qualifiers — that the two forces act on different objects and are of the same type. Getting this right is a standard A-Level exam question, and OCR examiners will penalise any student who claims that the weight of a book and the normal force on it are a Third Law pair (they are not).

This lesson fixes the wording, works through canonical examples (walking, jet propulsion, gravitational attraction), and hunts down the common misconceptions.

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Statement of the Third Law

If body A exerts a force on body B, then body B exerts a force on body A that is equal in magnitude, opposite in direction, and of the same type.

Three essential features:

1. Two different bodies. The forces act on different objects — never on the same object.
2. Same type. If A pulls B gravitationally, B pulls A gravitationally. If A pushes B by contact, B pushes A by contact. A gravitational force is never "paired" with a contact force.
3. Simultaneous. Both forces exist at the same instant. There is no delay.

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Diagram — A Correct Third Law Pair

flowchart LR
  A[Body A] -->|"Force F(A→B)"| B[Body B]
  B -->|"Force F(B→A) = −F(A→B)"| A

Every valid Third Law pair looks exactly like this: two forces, one on each body, same magnitude, opposite directions, same mechanism.

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Example 1 — Walking

When you walk, you push your foot backwards against the ground. The Third Law says the ground pushes your foot forwards by an equal amount. It is that forward force on you, from the ground, that propels you.

• Force on ground (from your foot): friction, backwards.
• Force on you (from the ground): friction, forwards.

Without friction (on an icy lake), you cannot walk — there is no force to push back against you. The Third Law does not fail; it is just that the forces involved are now much smaller.

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Example 2 — Jet and Rocket Propulsion

A jet engine pushes hot exhaust gas backwards. By the Third Law the gas pushes the engine forwards — this forward push is what we call thrust. Rockets work in exactly the same way, which is why they can accelerate in a vacuum: no atmosphere is needed, because the force is between the rocket and the exhaust gas, not between the rocket and the air.

• Force on exhaust gas (from the rocket): backwards.
• Force on rocket (from the exhaust gas): forwards.

Lesson 10 will return to rockets quantitatively using momentum conservation.

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Example 3 — Gravitational Attraction

The Earth pulls an apple downwards with a force m g ≈ 1 N (for a typical apple). The apple pulls the Earth upwards by the same 1 N. You do not notice the Earth accelerating towards the apple because the Earth has a mass of about 6 × 10²⁴ kg, so its resulting acceleration is astronomically tiny (about 10⁻²⁵ m s⁻²).

• Force on apple: 1 N downwards, gravitational.
• Force on Earth: 1 N upwards, gravitational.

Both forces are gravitational, satisfying the "same type" requirement.

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Example 4 — Book on a Table: the Classic Trap

A 2.0 kg book lies at rest on a table.

Forces on the book:

• Weight W = m g = 19.6 N downwards (from Earth's gravity).
• Normal contact force N = 19.6 N upwards (from the table).

Students constantly claim that W and N are a Third Law pair. They are not. Here is why:

• W and N act on the same object (the book). A Third Law pair must act on different objects.
• W is gravitational; N is a contact force. Different types.

W and N balance because the book is in equilibrium — this is the First Law, not the Third.

The true Third Law pairs are:

• Book pulls Earth gravitationally, Earth pulls book gravitationally (W).
• Book pushes table by contact, table pushes book by contact (N).

Name of force	Acts on	Type	Third Law partner
Weight of book W	Book	Gravity	Gravitational pull of book on Earth
Normal force on book N	Book	Contact	Contact push of book on table

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Example 5 — A Horse Pulling a Cart

An old paradox: "If the cart pulls the horse back with a force equal to the horse pulling the cart forward, how do they ever move?"