---
title: "Equal and Opposite Forces — AP Physics C Definition"
description: "Newton's third law: interacting objects exert equal-magnitude, opposite-direction forces on each other. Key for AP Physics C dynamics, tension, and momentum."
canonical: "https://fiveable.me/ap-physics-c-mechanics/key-terms/equal-and-opposite-forces"
type: "key-term"
subject: "AP Physics C: Mechanics"
unit: "Unit 2"
---

# Equal and Opposite Forces — AP Physics C Definition

## Definition

Equal and opposite forces is the core of Newton's third law: when object A exerts a force on object B, B exerts a force on A that is equal in magnitude and opposite in direction. The two forces act on DIFFERENT objects, so they never cancel each other on a single free-body diagram.

## What It Is

"Equal and opposite forces" is shorthand for [Newton's third law](/ap-physics-c-mechanics/unit-2/3-newtons-third-law/study-guide/SXl4nBHlUrotvxSj "fv-autolink"), covered in Topic 2.3 of [AP Physics C: Mechanics](/ap-physics-c-mechanics "fv-autolink"). Forces always come in interaction pairs. If object A pushes or pulls on object B with force F, then object B simultaneously pushes or pulls back on A with force -F. Same magnitude, opposite direction, same type of force (both gravitational, both normal, both friction), acting along the same line.

The detail that trips everyone up is that the two forces in a third-law pair act on **different objects**. The Earth pulls down on you; you pull up on the Earth. Those forces are equal and opposite, but they don't cancel because they're not acting on the same thing. What CAN differ wildly is the resulting acceleration. A 70 kg astronaut pushing off a 700 kg satellite feels the same 100 N the satellite does, but by Newton's second law the astronaut accelerates 10 times faster because acceleration is force divided by [mass](/ap-physics-c-mechanics/key-terms/mass "fv-autolink").

## Why It Matters

This lives in **Topic 2.3 (Newton's Third Law)** within [Unit 2](/ap-physics-c-mechanics/unit-2 "fv-autolink"), Force and Translational Dynamics, but it quietly powers half the course. Every free-body diagram you draw depends on correctly identifying which force in a pair belongs on which object. [Tension](/ap-physics-c-mechanics/key-terms/tension "fv-autolink") problems, normal force problems, and connected-body systems (blocks tied by strings, masses over pulleys) all require you to keep third-law pairs straight. It's also the microscopic reason momentum is conserved later in the course. Internal forces between objects in a system come in equal and opposite pairs, so they sum to zero and can't change the system's total momentum. If you ever wonder why conservation of momentum works, the answer is Newton's third law.

## Connections

### [Tension (Unit 2)](/ap-physics-c-mechanics/key-terms/tension)

Tension in a string is a third-law pair in action. The string pulls on the block, and the block pulls back on the string with equal [magnitude](/ap-physics-c-mechanics/unit-1/1-scalars-and-vectors/study-guide/rVQeOgdT8itcgCoV "fv-autolink"). For a massless string, this is why tension transmits force unchanged from one end to the other.

### [Internal Forces (Unit 2)](/ap-physics-c-mechanics/key-terms/internal-forces)

When you treat several objects as one [system](/ap-physics-c-mechanics/unit-2/1-properties-and-interactions-of-a-system/study-guide/Hw10Krhy0qtfeWAb "fv-autolink"), the forces they exert on each other are internal, and every internal force has an equal-and-opposite partner inside the system. They cancel in pairs, which is exactly why you can ignore them when applying F = ma to the whole system.

### [Ideal Pulley (Unit 2)](/ap-physics-c-mechanics/key-terms/ideal-pulley)

A massless, frictionless pulley just redirects the string. The equal-and-opposite logic of tension means the tension magnitude is the same on both sides, which is the assumption every [Atwood machine](/ap-physics-c-mechanics/key-terms/atwood-machine "fv-autolink") problem rests on.

### Conservation of Linear Momentum (Unit 4)

Two astronauts pushing off each other in space feel equal and opposite forces for the same time, so they get equal and opposite impulses. That's conservation of momentum derived from the third law in one step, and it's a favorite exam setup.

## On the AP Exam

Multiple-choice questions love the ratio setup. A classic stem gives two interacting objects of different masses (an astronaut pushing off a satellite, two ice skaters pushing apart) and asks for the ratio of their accelerations or velocities. The trick is that the forces are equal, so the acceleration ratio is just the inverse mass ratio. A 70 kg astronaut and a 700 kg satellite share the same 100 N force, so the astronaut's acceleration is 10 times larger. Impulse versions work the same way: equal forces for equal times mean equal and opposite momentum changes, so the speed ratio is the inverse mass ratio. No released FRQ has used the phrase verbatim, but third-law reasoning shows up constantly in FRQ free-body diagrams and connected-object problems. You lose points if you draw both members of a force pair on the same object or claim they "cancel." When justifying conservation of momentum in an FRQ, citing equal and opposite internal forces is exactly the reasoning graders want.

## Equal and opposite forces vs Balanced forces (equilibrium)

Balanced forces are different forces acting on the SAME object that happen to sum to zero, like gravity and the normal force on a book sitting on a table. A third-law pair is the same interaction viewed from both sides, acting on DIFFERENT objects. The book's weight and the table's normal force on the book are NOT a third-law pair; the partner of the normal force is the book pushing down on the table. Test it by asking which object each force acts on. If both act on the same object, it's not a third-law pair.

## Key Takeaways

- Newton's third law says that when two objects interact, each exerts a force on the other that is equal in magnitude and opposite in direction.
- The two forces in a third-law pair act on different objects, so they never appear on the same free-body diagram and never cancel each other.
- Equal forces do not mean equal accelerations; by F = ma, the less massive object accelerates more, so a 70 kg astronaut pushing a 700 kg satellite accelerates 10 times faster.
- Internal forces within a system cancel in third-law pairs, which is why conservation of momentum works for isolated systems.
- The normal force on a book and the book's weight are balanced forces, not a third-law pair; the partner of each force lives on the other object in the interaction.

## FAQs

### What does equal and opposite forces mean in AP Physics C?

It's Newton's third law: when object A exerts a force on object B, B exerts a force on A with equal magnitude and opposite direction. The two forces act on different objects, are the same type of force, and exist simultaneously.

### If forces are always equal and opposite, why does anything ever accelerate?

Because the paired forces act on different objects, each object's free-body diagram only contains one of them. An object accelerates based on the net force acting on it alone, so third-law pairs never cancel for a single object.

### Are weight and normal force a Newton's third law pair?

No. Both act on the same object (the book), so they can't be a third-law pair. The partner of the table's normal force on the book is the book pushing down on the table; the partner of Earth's gravity on the book is the book's gravitational pull on Earth.

### Do equal and opposite forces cause equal accelerations?

No. The forces are equal, but acceleration equals force divided by mass, so the lighter object accelerates more. Two skaters pushing off each other feel the same force, but the 50 kg skater speeds up faster than the 80 kg skater.

### How does Newton's third law connect to conservation of momentum?

Interacting objects exert equal and opposite forces for the same contact time, so they receive equal and opposite impulses. Their momentum changes cancel, which means the total momentum of an isolated system stays constant. That's the Unit 4 conservation law in one sentence.

## Related Study Guides

- [2.3 Newton's Third Law](/ap-physics-c-mechanics/unit-2/3-newtons-third-law/study-guide/SXl4nBHlUrotvxSj)

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