Action and reaction: the third law

You can't push anything without being pushed back. Not as karma — as mechanics, exactly, and instantly.

The law

When A exerts a force on B, B exerts a force on A that is equal in magnitude and opposite in direction.

Forces never come alone; they come as pairs across an interaction. Hammer hits nail, nail hits hammer (that's why it bounces). Earth pulls you down, you pull Earth up with the very same force.

Why the pair never cancels

"Equal and opposite — don't they cancel out?" No, and the reason is the whole lesson:

The two forces act on different objects. The skater's push acts on the wall; the wall's push acts on the skater. To predict the skater's motion you add up only the forces on the skater — and in that list, the pair's other half never appears. Forces cancel only when both act on the same body, like the balanced arrows in the first-law lesson. Confusing those two situations is the most common error in all of introductory mechanics.

The reaction is how everything moves

Look around: almost nothing propels itself directly. Everything pushes backward on something and rides the reaction:

• You walk by pushing the ground backward; the ground pushes you forward.
• A car's tires push the road backward; the road pushes the car ahead.
• A rocket throws exhaust down; the exhaust pushes the rocket up — no road, no air, no problem. (Rockets work better in vacuum.)

And the Earth–you pair? Same force, wildly different masses: your pull gives the planet an acceleration of about 10⁻²² m/s². The law is symmetric; the consequences follow F = ma.

Why this matters

The third law is conservation of momentum wearing work clothes: equal and opposite forces, acting for the same instant, transfer momentum without creating or destroying it. That's the final module.