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What is Newton's Third Law?

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University Course Reader · STEM

By Newton’s third law, the thrust exerted on the rocket is equal and opposite to the momentum of the expelled exhaust.

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Overview

When one object pushes another, the second pushes back just as hard in the opposite direction, so forces always come in pairs. Push a wall and the wall pushes you. The detail most people miss is that the two forces act on different objects, which is exactly why they don't cancel.
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Overview

Push something and it pushes back exactly as hard, every time, no exceptions. Forces travel in pairs like they're scared to go out alone. The part that trips everyone up: those two forces land on two different objects, which is why they don't cancel and why anything moves at all. 😎

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Detail

Push a box with 50 newtons and the box pushes back on you with 50 newtons, equal in size, opposite in direction, at the same instant. Forces cancel only when they act on the same object, and here one acts on the box while the other acts on you, so the box accelerates while you feel the reaction in your arms. Walking uses this directly: a shoe pushes the ground backward and the ground pushes the shoe forward, and that forward push is what moves you. On ice the shoe slides instead of gripping, so it never pushes the ground, and a push that never happens produces no push back. A rocket does not need a ground at all, because it pushes against its own exhaust: the engine throws gas backward, and the gas pushes the rocket forward. That is why a rocket still works in space. Equal forces do not produce equal results, because the same force accelerates a light object far more than a heavy one.
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Detail

Push a box with 50 newtons and the box pushes you with 50 newtons, so why isn't the universe frozen? Because forces only cancel when they hit the SAME object — your push lands on the box, the reaction lands on you, box moves. Walking is that same trade: your shoe shoves the ground backward, the ground shoves you forward. On ice your shoe just slides, so it never shoves anything, so nothing shoves you, hence the flailing. Rockets skip the problem by bringing their own stuff to throw, sending exhaust backward so the rocket goes forward, no ground required. What the law never promised is equal outcomes: two skaters shove off each other with the same force, but the 30-kilo kid rockets backward while the 90-kilo adult barely drifts.

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Analogy

Water leaving a fire hose nozzle at full pressure pushes the hose backward hard enough to knock an adult down, so crews brace their stance before opening the valve and work the nozzle in pairs. A line dropped at full pressure whips around the street on its own. The water fights the fire, and the crew spends real strength on the force fighting back.
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Analogy

Stepping off a small boat onto the dock, you push the boat backward to launch yourself forward, and it only works because the boat pushes you forward just as hard. On land the thing you push is bolted to a planet and doesn't budge, but a boat is loose in the water, so the same push sends it backward far more than it sends you forward. Physics gave you a free push and charged you a wet phone.
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Formal definition — The same term, explained the usual way

Newton's third law states that for every force exerted by one body upon a second, the second exerts a force of equal magnitude and opposite direction upon the first. The paired forces act on distinct bodies and therefore do not cancel. Resulting accelerations are inversely proportional to the respective masses.

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