2.3 Newton's Third Law

Newton's third law says that when two objects interact, they push or pull on each other with equal force in opposite directions. The key catch is that these paired forces act on different objects, so they never cancel out.

Why This Matters for the AP Physics 1 Exam

Newton's third law gives you the language to describe interactions between two objects, which shows up constantly when you build free-body diagrams and reason about forces. On the AP Physics 1 exam, you need to label paired forces correctly using "agent on object" notation and explain why those forces act on separate objects.

This topic also supports the kind of qualitative reasoning the exam rewards in its translation question, where you describe a scenario in words, justify a claim, and connect that reasoning to equations. Being able to identify which forces are internal versus external, and explaining why internal forces do not move a system's center of mass, is exactly the type of conceptual claim and evidence the exam looks for. You will also use tension and pulley ideas as building blocks in later force and energy problems.

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Key Takeaways

• Forces always come in pairs: $\vec{F}_{A \text{ on } B} = -\vec{F}_{B \text{ on } A}$, equal in magnitude and opposite in direction.
• Paired forces act on two different objects, so they cannot cancel each other.
• Internal forces inside a system come in third-law pairs and do not change the motion of the system's center of mass.
• Only a nonzero net external force can change the motion of a system's center of mass.
• In an ideal string (negligible mass, no stretch), tension is the same at every point; in a string with real mass, tension can vary.
• An ideal pulley has negligible mass and negligible friction, so tension stays the same on both sides.

Newton's Third Law Interactions

Paired Forces Between Objects

When two objects interact, they exert equal and opposite forces on each other. The math version of this law is:

$\vec{F}_{A \text{ on } B} = -\vec{F}_{B \text{ on } A}$

A few rules that always hold:

• These paired forces are often called action-reaction pairs.
• The two forces always act on different objects.
• They happen at the same time and cannot cancel each other, because they are exerted on separate objects.

Representing Third-Law Pairs

To represent a third-law pair, label each force by its agent and object: $\vec{F}_{A\text{ on }B}$ and $\vec{F}_{B\text{ on }A}$. These two forces are equal in magnitude and opposite in direction, but they act on different objects.

For a book sitting on a table, one third-law pair is $\vec{F}_{\text{table on book}}$ (pointing up) and $\vec{F}_{\text{book on table}}$ (pointing down). On separate free-body diagrams, you draw only the forces acting on that one object. So $\vec{F}_{\text{table on book}}$ shows up only on the book's diagram, and $\vec{F}_{\text{book on table}}$ shows up only on the table's diagram.

Common third-law pairs:

• Gravitational pair (the only at-a-distance interaction in AP Physics 1): Earth pulls the book down, and the book pulls Earth up.
• Normal-force pair: A table pushes up on a book, and the book pushes down on the table.
• Tension pair: A rope pulls on a box, and the box pulls on the rope.
• Friction pair: A foot pushes backward on the ground, and the ground pushes forward on the foot.

Each force in these pairs is exerted by one object on the other object in the interaction.

Internal Forces and Center of Mass

• Internal forces are interactions between objects within a system, and they come in equal and opposite third-law pairs.
• The center of mass is the point where you can treat the system's whole mass as being concentrated.
• Internal forces do not change the motion of the center of mass, because the paired internal forces add up to zero.
• Only external forces, exerted by objects outside the system, can change the motion of the center of mass.

Example: in a collision between two objects inside the same system, the action-reaction forces between them are internal, so they do not alter the motion of the system's center of mass.

Tension in Strings and Cables

• Tension acts along the length of a string, cable, or chain in response to an external force.
• Tension is the macroscopic result of the forces that segments of the string exert on each other.
• The size of the tension depends on the external force applied.
• In an ideal string, tension is the same everywhere along its length.

Properties of Ideal Strings

• An ideal string has negligible mass, so its weight is ignored in calculations.
• An ideal string does not stretch under tension, so its length stays constant.
• Because the string has negligible mass and does not stretch, the tension is the same at every point along it.

Tension in Strings With Mass

• A string with real, nonnegligible mass can have tension that varies along its length.
• In a hanging chain or rope with mass, the tension is greater toward the top than toward the bottom, since the upper part supports more weight below it.

This is the qualitative reasoning the exam expects for strings with mass: you should be able to describe how tension changes along the object, not calculate exact values.

Ideal Pulleys

• An ideal pulley redirects the direction of a force.
• It has negligible mass and negligible friction, and it rotates about an axle through its center of mass.
• When a string passes over an ideal pulley, the tension is the same on both sides.

How to Use This on the AP Physics 1 Exam

Free Response

When a question asks you to identify a third-law pair, always name both objects using "agent on object" notation and state that the two forces are equal in magnitude and opposite in direction. Make it clear that the two forces act on different objects.

If you draw free-body diagrams for two interacting objects, remember each diagram shows only the forces on that one object. The two members of a third-law pair never appear on the same free-body diagram.

For the translation-style question, practice describing an interaction in words first, then connecting it to $\vec{F}_{A \text{ on } B} = -\vec{F}_{B \text{ on } A}$. A strong answer makes a claim, backs it with reasoning about paired forces, and links that reasoning to the equation.

Problem Solving

• For systems with internal collisions or pushes, identify the system boundary first. Forces inside the boundary are internal and cannot move the center of mass.
• Use ideal-string and ideal-pulley assumptions to set tension equal throughout, which simplifies multi-object setups.
• For a string or chain with mass, expect a qualitative answer about where tension is greatest, not a number.

Common Trap

A common mistake is treating the normal force and gravity on a single object as a third-law pair. They are not. Both act on the same object, and they are not always equal. A true third-law pair always involves two different objects.

Common Misconceptions

• "Action-reaction forces cancel out." They never cancel, because they act on two different objects. Forces only cancel when they act on the same object.
• "The larger object pushes harder." No. In any interaction, both objects feel forces equal in magnitude, even if one object is much more massive. The more massive object just accelerates less.
• "Gravity and the normal force on a book are a third-law pair." They are not. Both act on the book, and they can differ in size if the book is accelerating. The gravity pair is Earth and the book pulling on each other.
• "Internal forces can move the whole system." Internal third-law pairs always sum to zero, so they cannot change the motion of the system's center of mass. Only external forces can.
• "Tension is always the same in every rope." That is only true for an ideal, massless string. A rope or chain with real mass can have different tension at different points, usually greater toward the top.
• "An ideal pulley changes the tension." An ideal pulley only redirects the force. With negligible mass and friction, the tension stays the same on both sides.

Related AP Physics 1 Guides

• 2.1 Systems and Center of Mass
• 2.2 Forces and Free-Body Diagrams
• 2.4 Newton's First Law
• 2.5 Newton's Second Law
• 2.6 Gravitational Force
• 2.7 Kinetic and Static Friction