Newton's Third Law
You’re standing on roller skates in front of a wall. You push the wall with both hands. The wall doesn’t move — but you roll backward across the floor.
Wait. You pushed the wall. So why did you end up moving?
Because the wall pushed you back. Every force in the universe comes in a pair: when you push something, that something pushes back on you with the exact same strength. The wall didn’t move because it’s bolted to a building (lots of mass + lots of friction). You did move, because nothing was holding you in place. Same forces — wildly different outcomes.
That’s Newton’s third law. The single biggest mistake students make is forgetting that the two paired forces act on different objects.
The Law
The two forces in an action-reaction pair are always:
- Equal in magnitude. Same number of newtons.
- Opposite in direction. They point away from each other.
- On different objects. This is the part students forget.
- Of the same type. Both gravitational, both contact, both electrical, etc. (You can’t pair gravity with friction.)
The Critical Misconception
Students constantly ask: “If every force has an equal and opposite reaction, why doesn’t everything just cancel and nothing ever accelerates?”
The answer: the two forces act on different objects. Forces only cancel when they’re on the same object.
You push the wall (force on the wall). The wall pushes you (force on you). When you draw a free-body diagram for yourself, only the force on you appears. The force you put on the wall doesn’t show up on your FBD — it shows up on the wall’s FBD. Action-reaction pairs live on separate diagrams. They literally cannot cancel each other.
Identifying Action-Reaction Pairs
To find a reaction force, swap the two objects and reverse the direction. The grammar is “A pushes/pulls B” → “B pushes/pulls A in the opposite direction.”
| Action (force on B by A) | Reaction (force on A by B) |
|---|---|
| You push wall east | Wall pushes you west |
| Earth pulls you down (gravity) | You pull Earth up (gravity) |
| Hammer hits nail down | Nail pushes hammer up |
| Foot pushes ground back | Ground pushes foot forward (friction) |
| Rocket pushes exhaust gas down | Exhaust gas pushes rocket up |
Walking: The Third Law in Action
How do you actually walk? Your foot pushes backward on the ground; the ground pushes forward on your foot (that’s just friction). The forward push on your foot is the only horizontal force on your body, and it’s what accelerates you forward.
On slippery ice, your foot still pushes backward — but the ice can’t push you forward (no friction). Result: your foot slides backward and you don’t go anywhere. Without the reaction force, you can’t accelerate. Walking is Newton’s third law.
The same logic explains how cars drive (tires push road back, road pushes car forward), how swimmers swim (hands push water back, water pushes swimmer forward), and how planes fly (wings push air down, air pushes wings up).
Why the Earth Doesn’t Noticeably Move When You Jump
When you jump, you push the Earth downward and the Earth pushes you upward — equal forces, by the third law. So why does only one of you move?
Because the Earth’s mass is about kg. Plug that into and the Earth’s acceleration comes out to a number so absurdly small (about m/s²) that no instrument on Earth could ever detect it. You accelerate by several m/s²; the Earth accelerates by basically nothing — but the forces are equal. Mass, not force, is what determines who actually moves.