AP Physics 1 · Unit 2: Forces & Translational Dynamics · Lesson 2.3

Deep Dive: Newton's Third Law

🔬 Deep Dive

This is your textbook for this topic. Take your time. Read it more than once.

2.3.A.1ConceptMath

The Law of Paired Forces

When two objects interact, they exert forces on each other that are equal in magnitude and opposite in direction. This is Newton's Third Law, and it can be written precisely using agent-on-object notation:

F⃗(A on B) = −F⃗(B on A)

Read this as: "the force of A on B equals negative the force of B on A." The negative sign means the directions are opposite. The magnitudes are exactly the same — always, no exceptions, regardless of the masses of A and B.

🔑These two forces act at the same time, as part of one single interaction. There's no "first" force that causes a "second" reaction — they happen simultaneously, which is why "action-reaction" can be a slightly misleading name even though it's commonly used.

2.3.A.1.i⚠ Watch Out

Spotting a Real Third-Law Pair

This is where most students lose points. Two forces that look similar — same size, opposite direction — are not automatically a third-law pair. The single test that matters: do the two forces act on two different objects?

✗ Not a pair

✓ Real pair

⚠️The classic exam trap: normal force and weight on the same object look like a matched pair — equal size, opposite direction. They are not a third-law pair, because they both act on the same object (the book). They happen to balance because the book isn't accelerating — that's Newton's First Law, not the Third.

ExampleWorked Example — Identifying the Pair

A 60 kg swimmer pushes off a pool wall with 300 N of force. What is the third-law pair to this force, and what does the swimmer experience as a result?

2.3.A.2Concept

Why Internal Forces Cancel

You saw this idea back in Lesson 2.1: internal forces between objects in the same system always cancel when you add up all the forces on that system. Now you know why — it's a direct consequence of Newton's Third Law. Every internal force has an equal and opposite partner inside the same system, so they sum to zero.

💡When two skaters push off each other, the push between them is an internal third-law pair. It changes each skater's individual motion — but it cannot move the system's overall center of mass, because the two forces cancel when you consider both skaters as one system.

This is also why you can't pull yourself forward by pulling on your own shirt. Any force you exert on yourself is internal to the "you" system — its third-law partner acts on you too, and the two cancel completely.

2.3.A.3Concept

Tension Is Newton's Third Law in Disguise

Tension is the pulling force transmitted through a rope, string, cable, or chain. At the macroscopic level it feels like one smooth pull — but it's actually the net result of countless tiny segments of the string pulling on their neighbors, each pair obeying the third law.

🔑A string can only pull, never push. In any free-body diagram, the tension vector always points away from the object, along the direction of the string.

💡A hanging chain: tension is qualitatively greater near the top of the chain. The top link has to support the weight of every link below it, while the bottom link only supports itself. This is a qualitative reasoning point the AP exam tests — you won't need to calculate exact values, just explain the trend.

2.3.A.4ConceptMath

Ideal Strings and Ideal Pulleys

AP Physics 1 almost always uses the ideal versions of strings and pulleys — simplified models that make the math dramatically easier without losing the physics that matters.

Component	Ideal assumption	What it means
Ideal string	Negligible mass, doesn't stretch	Tension is the same at every point along the string
Ideal pulley	Negligible mass, negligible friction	Tension is identical on both sides — the pulley only redirects the force

Pull the rope with different forces. Watch how the tension stays identical on both sides of an ideal (massless, frictionless) pulley.

Applied force20 N

Left side: 20 N =  Right side: 20 N✓ Always equal — that's what "ideal" means

When a string has real, non-negligible mass — a heavy rope instead of a light string — tension can vary along its length. You won't need to calculate exact values for these cases, but you should be able to reason qualitatively about where tension is greater or smaller.

ExampleGuided Example — Two Blocks Over an Ideal Pulley

A 3 kg block hangs from a light string over a frictionless pulley, connected to a 2 kg block resting on a frictionless table. What is the tension in the string?

Step 1 — Set up the system

Define down as positive for the hanging 3 kg block, and the direction of motion as positive for the 2 kg block. Since they're connected by an ideal string over an ideal pulley, both blocks share the same magnitude of acceleration, and the tension is identical throughout the string.

← Back to Lesson 2.3 Next: Lesson 2.4 →Newton's First Law explains why objects resist changes to their motion.

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