AP Physics C: Mechanics · Unit 2: Force and 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.1Concept

Newton's Third Law: Paired Forces

Newton's third law describes every interaction between two objects or systems in terms of a matched pair of forces: if object A exerts a force on object B, then object B exerts an equal-magnitude, opposite-direction force back on A. Neither force causes the other — they exist simultaneously, as two faces of one interaction.

🔑The single most important detail: the two forces in a third-law pair act on two different objects. If both forces you're looking at act on the same object, they cannot be a third-law pair — no matter how equal and opposite they happen to look.

This is exactly why normal force and gravity, both acting on a block resting on a table, are not a third-law pair — even in the common case where they happen to be equal in magnitude.

BlockN⃗ (table on block)m g⃗ (Earth on block)✕ NOT a 3rd-law pairBoth forces act on theSAME object (the block).Different interactions —table vs. Earth — that justhappen to balance.
⚠️The actual third-law partner of the normal force the table exerts on the block is the force the block exerts back on the table — a completely different force, acting on a completely different object, that never even shows up on the block's own free-body diagram.

Try it yourself below — three classic scenarios, each with its two paired forces drawn on the two different objects involved.

Pick a scenario — both force arrows are always equal in length and opposite in direction, each one acting on a different object.

HandWallF⃗(Hand on Wall)F⃗(Wall on Hand)Equal magnitude · opposite direction · two different objects
ExampleGuided Example — The Tug-of-War Puzzle

In a tug-of-war, the tension in the rope is genuinely the same at both ends (it's one ideal string). So why does one side usually still win?

Step 1Identify the third-law pair
The rope pulls each person with the same tension T — this is the string's ideal-tension property, not yet Newton's third law.
2.3.A.2Concept

Internal Forces and the Center of Mass

Because every internal interaction inside a system comes as a third-law pair, those forces always cancel out when you sum up the net force on the whole system. Internal forces cannot change a system's center-of-mass motion — only external forces can.

💡This is exactly why the tug-of-war puzzle resolves the way it does: the rope tension is internal to the two-person-plus-rope system, so it can never determine which way that system accelerates. Only the external friction forces from the ground can do that.
2.3.A.32.3.A.3.i2.3.A.3.iiConcept

Tension in Ideal Strings

Tension isn't a fundamental force of its own — it's the macroscopic, net result of countless infinitesimal segments of a string, cable, or chain pulling on their neighbors in response to an external force stretching the string taut.

An ideal string makes two simplifying assumptions that make tension problems tractable:

Mass of ideal string ≈ 0  ·  Does not stretch
🔑Because an ideal string has no mass, Newton's second law applied to any tiny piece of it gives zero net force on that piece — which forces the tension to be exactly the same at every point along the string's length. This is why you can talk about "the tension" in a problem as a single number.
2.3.A.3.iii2.3.A.3.ivConcept

When Strings Have Mass, and Ideal Pulleys

Real ropes have mass, and once they do, the "same tension everywhere" shortcut breaks down. A point higher up a hanging rope has to support not just whatever's hanging below it, but also the weight of all the rope between it and the bottom — so tension increases as you move up a massive hanging rope.

Compare the two cases directly below.

A rope holds a 5 kg mass, hung from a fixed support. Toggle between an ideal string (negligible mass) and a real rope with 3 kg of its own mass distributed along its length.

5 kg
T at bottom = 50 N
T at top = 50 N

Ideal string: tension is identical at every point, top to bottom.

Ideal pulleys

An ideal pulley makes its own pair of simplifying assumptions: negligible mass, and an axle that rotates with negligible friction. Together, these mean an ideal pulley doesn't change the magnitude of tension in a string passing over it — it only redirects the string's direction. This is exactly what lets you treat tension as a single shared value across every ideal string segment in a pulley system like the three-mass setup from this unit's header image.

⚠️If a problem gives a pulley mass or explicitly mentions friction at the axle, the "same tension on both sides" shortcut no longer applies — that's usually a strong signal the problem wants you to bring in rotational dynamics from Unit 5 instead.
← Back to Lesson 2.3Ready for 2.4? Newton's First Law puts everything you know about balanced forces into a single condition: equilibrium.