Newton's Third Law: Identify Action–Reaction Pairs

On this page: The Principle · Conditions · Misconceptions · EE Questions · Retrieval Practice · Worked Example · Solve a Problem · FAQ

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The Principle

Statement

Whenever one object exerts a force on a second object, the second object simultaneously exerts a force of equal magnitude and opposite direction on the first object. In common phrasing, “for every action, there is an equal and opposite reaction.” Think interaction pair, not “action then reaction”—the two forces are two sides of the same single interaction.

Mathematical Form

$\vec{F}_{AB} = -\vec{F}_{BA}$

Where:

• $\vec{F}_{AB}$ = force exerted by object A on object B (Newtons, $\mathrm{N}$)
• $\vec{F}_{BA}$ = force exerted by object B on object A (Newtons, $\mathrm{N}$)
• The negative sign indicates the vectors point in opposite directions.

Alternative Forms

In different contexts, this appears as:

• Scalar Magnitude: $|F_{AB}| = |F_{BA}|$
• Component Form: $F_{AB,x} = -F_{BA,x}$

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Conditions of Applicability

Condition: Newtonian

Practical modeling notes (optional)

• Pair test: If one force is “A on B”, the matching force must be “B on A” and of the same interaction type (e.g., both are gravitational).
• Simultaneity: In introductory mechanics, we treat the pair as simultaneous. The forces appear and disappear at exactly the same time.
• Single Interaction: Both forces are part of the same physical interaction (e.g., both are gravitational, or both are contact forces).
• Different Objects: The most critical rule for modeling is that the interaction forces act on two different objects. They never act on the same object. This is why internal forces don’t change system momentum → Conservation of Linear Momentum.

Want the complete framework behind this guide? Read Masterful Learning.

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Common Misconceptions

Misconception 1: “Action-Reaction forces cancel out”

The truth: Because action and reaction forces act on different objects, they never appear in the same free-body diagram and therefore cannot cancel each other out.

Why this matters: They don’t cancel on a single object because they act on different objects. Acceleration happens because the net force on a single object is non-zero.

Misconception 2: “The reaction force happens slightly after the action”

The truth: In introductory mechanics we treat the interaction pair as simultaneous—neither force happens after the other.

Why this matters: Students often look for a “response” from an object, but the force is present the instant the contact or field interaction begins.

Misconception 3: “A stronger or faster object exerts more force”

The truth: When a massive truck hits a small bug, the truck exerts exactly the same amount of force on the bug as the bug exerts on the truck. Same force, different acceleration → Newton’s Second Law.

Why this matters: The effect (acceleration) is different because of Newton’s Second Law ($a = F/m$), but the forces are identical in magnitude.

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Elaborative Encoding

Use these questions to build deep understanding. (See Elaborative Encoding for the full method.)

Within the Principle

• What is the physical meaning of the negative sign in $\vec{F}_{AB} = -\vec{F}_{BA}$?
• If the magnitude of $\vec{F}_{AB}$ is $10\,\mathrm{N}$, what must be the magnitude of $\vec{F}_{BA}$?

For the Principle

• If you are drawing a free-body diagram for a single block, should you include both forces of an action-reaction pair? Why or why not?
• How can you verify if two forces are a “pair”? (Hint: Swap the “giver” and “receiver” labels).

Between Principles

• How does Newton’s Third Law explain why a propeller can push a plane forward through the air? (Contrast with Newton’s Second Law).

Generate an Example

• Describe a situation involving a magnet and a piece of iron where the forces are equal and opposite, even though the iron moves much more than the magnet.

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Retrieval Practice

Answer from memory, then click to reveal and check. (See Retrieval Practice for the full method.)

State the principle in words: _____If object A exerts a force on object B, then object B exerts a force of equal magnitude and opposite direction on object A.

Write the canonical equation: _____$\vec{F}_{AB} = -\vec{F}_{BA}$

State the canonical condition: _____Newtonian

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Worked Example

Use this worked example to practice Self-Explanation.

Problem

A $70\,\mathrm{kg}$ ice skater pushes off a $200\,\mathrm{kg}$ crate on frictionless ice. If the skater exerts a constant horizontal force of $140\,\mathrm{N}$ on the crate, what is the magnitude of the skater’s acceleration?

Step 1: Verbal Decoding

Target: $a_S$
Given: $m_S, m_C, F_{SC}$
Constraints: frictionless, horizontal, simultaneous interaction

Step 2: Visual Decoding

Try drawing the skater and the crate. Draw a 1D axis. Choose $+x$ to the right (the direction the skater pushes the crate). Label the force on the crate $F_{SC}$ along $+x$ and the force on the skater $F_{CS}$ along $-x$.

(So $F_{SC}$ is positive and $F_{CS}$ is negative.)

Step 3: Physics Modeling

1. $\vec{F}_{CS} = -\vec{F}_{SC}$
2. $\sum F_{S,x} = F_{CS,x} = m_S a_{S,x}$

Step 4: Mathematical Procedures

1. $|F_{CS}| = |F_{SC}|$
2. $|a_S| = \frac{|F_{CS}|}{m_S}$
3. $|a_S| = \frac{140\,\mathrm{N}}{70\,\mathrm{kg}}$
4. $\underline{|a_S| = 2\,\mathrm{m/s^2}}$

Step 5: Reflection

• Units: $\mathrm{N/kg} = (\mathrm{kg \cdot m/s^2})/\mathrm{kg} = \mathrm{m/s^2}$, which matches acceleration.
• Magnitude: $2\,\mathrm{m/s^2}$ is a reasonable acceleration for a skater.
• Limiting case: If the skater’s mass $m_S$ were much larger, the acceleration $a_S$ would approach zero for the same push.

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Before moving on: self-explain the model

Try explaining Step 3 out loud (or in writing): why the chosen principle applies, what the diagram implies, and how the equations encode the situation.

Physics model with explanation (what “good” sounds like)

Principle: Newton’s Third Law and Newton’s Second Law.

Conditions: The “Always applies” condition for the Third Law is met for the interaction. The “Net force” condition for the Second Law is met by considering the horizontal forces on the skater.

Relevance: To find the skater’s acceleration, we need the force acting on the skater. The problem only gives the force the skater exerts on the crate. The Third Law provides the bridge to find the reciprocal force.

Description: The skater and crate interact. By the Third Law, the crate pushes back on the skater with $140\,\mathrm{N}$ in the opposite direction.

Goal: We find the reaction force magnitude, then use the Second Law to calculate the resulting acceleration of the skater’s mass.

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Solve a Problem

Apply what you’ve learned with Problem Solving.

Problem

A $0.2\,\mathrm{kg}$ apple is falling toward Earth. The Earth exerts a gravitational force of $1.96\,\mathrm{N}$ on the apple. What is the magnitude of the force that the apple exerts on the Earth?

Hint (if needed): Remember that Newton’s Third Law applies to all interactions, including those involving gravity and massive planets.

Show Solution

Step 1: Verbal Decoding

Target: $F_{EA}$ (force of apple on Earth)
Given: $m_A, F_{AE}$ (force of Earth on apple)
Constraints: gravitational interaction, falling

Step 2: Visual Decoding

Try drawing the Earth and the apple. Choose $+y$ as upward. Label the force on the apple $F_{AE}$ pointing down (negative) and the force on the Earth $F_{EA}$ pointing up (positive).

(So $F_{AE}$ is negative and $F_{EA}$ is positive.)

Step 3: Physics Modeling

1. $\vec{F}_{EA} = -\vec{F}_{AE}$

Step 4: Mathematical Procedures

1. $|F_{EA}| = |F_{AE}| = 1.96\,\mathrm{N}$
2. $\underline{|F_{EA}| = 1.96\,\mathrm{N}}$

Step 5: Reflection

• Units: Force is correctly given in Newtons ($\mathrm{N}$).
• Magnitude: The force is identical to the weight of the apple, as required by the law.
• Limiting case: The Earth’s acceleration resulting from this force is effectively zero due to its massive mass, but the force itself is not zero.

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Related Principles

Principle	Relationship to Newton’s Third Law
Newton’s First Law	To kill the “they cancel so nothing moves” misconception.
Newton’s Second Law	Connects the forces found via the Third Law to the acceleration of individual objects.
Impulse-Momentum Theorem	Collision forces are big but short; use impulse reasoning.
Conservation of Momentum	The Third Law ensures that internal impulses cancel within a system.

See Principle Structures for how to organize these relationships visually.

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Next Step in Mechanics Core

• Next: Impulse–Momentum Theorem — force over time → momentum change

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FAQ

What is Newton’s Third Law?

Newton’s Third Law states that forces always exist in pairs. If object A exerts a force on object B, object B must exert a force of equal magnitude and opposite direction back on object A.

When does Newton’s Third Law apply?

It applies to every interaction in classical mechanics, without exception. Whether objects are touching (contact forces) or separated by a distance (field forces like gravity), the symmetry holds.

Why don’t action and reaction forces cancel out?

They don’t cancel because they act on different objects. To cancel out, two forces would need to act on the same object in opposite directions, resulting in a net force of zero for that object.

Is the Third Law true for gravity?

Yes. The Earth pulls on you with a force equal to your weight, and you simultaneously pull on the Earth with a force exactly equal to your weight.

How do I identify a Third Law pair?

A simple test is to identify the two objects involved. If Force 1 is “Object A on Object B,” then its pair must be “Object B on Object A.” If the objects are not swapped, it is not a Third Law pair.

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Related Guides

• Principle Structures — Organize this principle in a hierarchical framework
• Self-Explanation — Learn to explain worked examples step by step
• Retrieval Practice — Make this principle instantly accessible
• Problem Solving — Apply principles systematically to new problems

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How This Fits in Unisium

Mastering Newton’s Third Law requires more than just memorizing the “equal and opposite” phrase; it requires the ability to correctly identify interacting systems. The Unisium Study System helps you internalize this through elaborative encoding and retrieval practice, ensuring you never mistakenly cancel out interaction forces in your free-body diagrams.

Ready to master Newton’s Third Law? Start practicing with Unisium or explore the full learning framework in Masterful Learning.

Masterful Learning

The study system for physics, math, & programming that works: encoding, retrieval, self-explanation, principled problem solving, and more.

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