Newton's Third Law (Action-Reaction)

Newton's third law says that if object A exerts a force on object B, then object B exerts an equal-magnitude force in the opposite direction on object A. The two forces happen at the same time and act on different objects. For one interaction,

where the minus sign carries the "opposite direction" and the equal magnitudes carry "equal." A fast way to remember it: an interaction always has two sides, so never look for a third-law force without naming both objects first.

Why The Pair Does Not Cancel

The phrase "action-reaction" is a little misleading because it sounds sequential. In physics the pair is simultaneous. Just as important, the two forces do not act on the same object, which is exactly why they do not cancel on one free-body diagram. Forces cancel only when they act on the same object. The relation $\vec{F}_{A \text{ on } B} = -\vec{F}_{B \text{ on } A}$ is a statement about two different bodies, so the two sides live on two different diagrams and never sum on one.

Worked Example: Two Skaters Push Off

Two skaters stand on nearly frictionless ice. Skater A pushes skater B to the right with a force of $40\ \mathrm{N}$. At the same moment, skater B pushes skater A to the left with $40\ \mathrm{N}$:

These are a third-law pair: same interaction, opposite directions, equal magnitudes. If the skaters have different masses, their accelerations can still differ, and that does not break the law. The law fixes the forces as equal in magnitude, not the accelerations. By Newton's second law, $a = F_{net}/m$ for constant mass, so the smaller-mass skater gets the larger acceleration. Equal force with unequal mass produces unequal motion.

Spot The Pair, Then Check It Yourself

Run this short check on any candidate pair:

1. Name the two interacting objects.
2. Write one force clearly, such as "force of skater A on skater B."
3. Reverse the objects to get the partner force: "force of skater B on skater A."
4. Check that both forces come from the same interaction.
5. Confirm they act on different objects and point in opposite directions.

If any one check fails, you are probably not looking at a third-law pair. Try it on your own everyday interaction, such as pushing a wall or jumping off the floor: write the pair in words first, "force of you on the wall" and "force of the wall on you," before drawing anything. The one mental check that prevents most errors is the cancel test: if two equal and opposite forces seem like they should disappear, ask whether they act on the same object. If the answer is no, they are not a canceling pair on one free-body diagram.

Calculation Traps To Avoid

• Thinking the pair cancels because the forces are equal and opposite. They do not cancel unless they act on the same object.
• Treating "action" as first and "reaction" as later. The two forces are simultaneous.
• Matching the wrong forces. The reaction to your push on a wall is the wall's push on you, not your weight or the floor's normal force.
• Assuming equal forces must produce equal motion. Equal force with different mass can produce different acceleration.

Where You Use Newton's Third Law

The third law appears whenever two objects interact: walking, jumping, pushing a cart, swimming, or a rocket pushing exhaust backward. The exact motion still depends on the full force picture on each object. When you walk, your foot pushes backward on the ground and the ground pushes forward on you through friction; if the surface cannot provide enough friction, that forward push is too small and walking becomes hard.

Frequently Asked Questions