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Newton's Third Law of Motion

Classical Mechanics

Newton's third law is one of the most quoted and most misunderstood ideas in physics. It says that forces always come in pairs: whenever one object pushes or pulls on another, the second object pushes or pulls back with an equal force in the opposite direction. From walking and swimming to rockets lifting off, this pairing is behind almost every movement you make.

What the law says

Newton's third law states that for every action there is an equal and opposite reaction. If object A exerts a force on object B, then object B exerts a force on object A that is equal in size and opposite in direction. The two forces are called an action-reaction pair. They act on different objects, they are the same type of force, and they act at the same time. Neither force exists on its own: the pair is created together and disappears together, which is why a force can never be a one-sided event.

Why the forces do not cancel out

A common puzzle is this: if the forces are equal and opposite, why does anything move at all? The answer is that the two forces act on different objects, so they never cancel each other in the calculation for one object. When you push a box forward, the box pushes you backward with the same force, but the forward force acts on the box and the backward force acts on you. Each object responds to the force on itself. The box moves because the force on the box is unbalanced, and you stay put because friction between your shoes and the ground holds you in place.

Where you see it

Walking works because your foot pushes backward on the ground and the ground pushes you forward. A swimmer pushes water backward and the water pushes the swimmer forward. A rocket pushes hot gas downward out of its engines, and the gas pushes the rocket upward. When a bird flies, its wings push air down and the air pushes the wings up. Even a book resting on a table is a third-law pair: the book pushes down on the table with its weight, and the table pushes up on the book with a normal force.

Common mistakes

• Thinking action-reaction forces cancel each other out. Correction: they act on different objects, so each object feels only its own force.
• Pairing up forces that are not a pair. Correction: a true pair is the same type of force, between the same two objects, weight and the normal force on a book are not a pair.
• Saying the reaction happens after the action. Correction: the two forces act at exactly the same time.

Practice questions

1. You push a wall with a force of 80 N. What force does the wall exert on you?
   Show answer

   80 N in the opposite direction, the wall pushes you back with an equal and opposite force.

2. A rocket engine pushes exhaust gas down with a force of 5000 N. What is the thrust on the rocket?
   Show answer

   5000 N upward. The gas pushes the rocket up with a force equal and opposite to the force on the gas.

3. A 10 kg box is pushed with 40 N. The box pushes back on your hands with 40 N. Why does the box still move?
   Show answer

   The 40 N backward force acts on you, not on the box. The box feels only the 40 N forward push, so it accelerates.

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