Newton's Third Law
You cannot push without being pushed back
- Shove a heavy wall and you feel it shove you — hard enough and you slide backward.
- Every force is one half of a pair; there is no such thing as a lone push.
- Newton's third law: if A pushes B, then B pushes A equally and oppositely.
- This is why rockets fly, swimmers move, and you can walk at all.
The law in symbols
- For any interaction between two bodies: $\vec F_{A\to B} = -\,\vec F_{B\to A}$.
- Equal in size, opposite in direction — always, no exceptions.
- It holds whether the objects are still, moving, heavy, or light.
- The pair appears and disappears together, at the same instant.
You push a wall with a force of $50\ \text{N}$. With what force does the wall push back on you?
By the third law the reaction is equal in size: the wall pushes back with $50\ \text{N}$.
Newton's third law says forces come in equal-and-____ pairs.
Equal in magnitude, opposite in direction: $\vec F_{A\to B} = -\vec F_{B\to A}$.
The pair acts on different objects
- The two forces in the pair act on different bodies — one on A, one on B.
- That is why they do not cancel: cancellation only happens for forces on the same object.
- To find the motion of B, you only count the forces acting on B.
- The reaction force acts on A, so it never appears in B's free-body diagram.
The two forces of an action–reaction pair act on the same object.
They act on different objects — one on A, one on B. That is why they do not cancel.
Why do the action and reaction forces not cancel each other out?
Forces only cancel when they act on the same body. Action and reaction act on two different bodies.
Third law all around you
- Walking: your foot pushes the ground back; the ground pushes you forward.
- Swimming: you push water back; the water pushes you forward.
- Rockets: engines push gas down; the gas pushes the rocket up.
- In each case the small "reaction" is what actually drives you.
Third-law pairs
Newton's third-law forces are equal, opposite, and act on different objects. Sort each statement.
A rocket pushes exhaust gas backward with $2000\ \text{N}$. With what force does the gas push the rocket forward, in $\text{N}$?
The reaction is equal and opposite: the gas pushes the rocket forward with $2000\ \text{N}$ of thrust.
Select all examples that rely on Newton's third law.
Swimming, walking and rockets all push on something that pushes back. A resting book still has third-law pairs, but its motion is not driven by them.
Action and reaction never cancel each other out, because they act on different objects. A common mistake is to say "the forces are equal and opposite, so nothing moves". They are equal and opposite — but on two separate bodies, so each body can still accelerate.
A rocket engine pushes exhaust gas backward with $2000\ \text{N}$.
- By the third law, the gas pushes the rocket forward with $2000\ \text{N}$.
- That forward force on the rocket is the thrust that launches it.
Newton's third law: $\vec F_{A\to B} = -\vec F_{B\to A}$ — forces come in equal-and-opposite pairs. The two act on different objects, so they never cancel. Walking, swimming and rockets all work by pushing on something that pushes back.