Newton's third law — action-reaction, common misconceptions: Question bank

Before you start, keep the four S's from the parent note in mind — Swap the labels, Same the size, Split the bodies, Simultaneous in time. Almost every trap here is broken by one of those four words.

Notation & definitions you need first

Every symbol used on this page is built here before it appears in any question.

Recall Why

$d P / d t = 0$ gives the third law (the equivalence, derived) Assumptions: an isolated two-body system — only $A$ and $B$ , and the only forces they feel are from each other (nothing external). Then experiment says total momentum $P$ never changes. Constant means zero rate of change: $\frac{d P}{d t} = \frac{d p _{A}}{d t} + \frac{d p _{B}}{d t} = 0.$ By the second law each rate is the net force on that body, and the only force on $A$ is from $B$ : $\frac{d p _{A}}{d t} = F_{B \to A}$ and $\frac{d p _{B}}{d t} = F_{A \to B}$ . Substituting: $F_{B \to A} + F_{A \to B} = 0$ , i.e. $F_{A \to B} = - F_{B \to A}$ . See Conservation of Momentum.

True or false — justify

Every force in nature has a reaction partner.

True. A force is one half of an interaction between two bodies, so there is always a second body pushing back; a lonely force cannot exist.

A book on a table has its weight cancelled by the normal force, so weight and normal force are a 3rd-law pair.

False. Both act on the same body (the book) and are different force types (gravity vs contact) — they cancel by the second law equilibrium, not the third.

Action and reaction always have equal magnitude even when the two objects have very different masses.

True. Magnitude equality is guaranteed by the third law and does not depend on mass; only the resulting accelerations differ via

a = F / m

If the horse pulls the cart and the cart pulls back equally, the system can never accelerate.

False. Those two forces act on different bodies, so they never cancel; the cart+horse system accelerates because of the external forward friction from the ground.

A 3rd-law pair can appear together in a single free-body diagram.

False. The two forces act on two different bodies, so they belong to two separate free-body diagrams — seeing both in one diagram is the classic error.

When you clap, your right hand feels a bigger force because you swing it harder.

False. Whatever the motion, the two hands exert equal-magnitude forces on each other at every instant; "swinging harder" changes speed, not the equality of the pair.

Momentum conservation for an isolated pair is logically equivalent to the third law.

True.

d P / d t = 0

forces

F_{A \to B} = - F_{B \to A}

, and conversely — each implies the other, as derived above. See Conservation of Momentum.

Gravity's reaction partner is another gravitational force.

True. If Earth pulls the book down, the book pulls Earth up with equal magnitude — same type (gravity), swapped labels.

The third law only works for gravity and contact, not for electric or magnetic forces between charges.

False. Two charges attract/repel with equal-opposite forces too; for static charges the pair is collinear, so momentum is conserved exactly as with gravity (subtle exceptions appear only for fast-moving charges, where the field itself carries momentum).

A rocket needs air or ground to push against in order to accelerate.

False. The reaction partner is the ejected exhaust gas, not the surroundings; the rocket works in vacuum. See Rocket Propulsion & Variable Mass.

Spot the error

"The Earth pulls the apple down with 1 N, and the apple pulls the Earth up with a much smaller force because Earth is huge."

The magnitudes are exactly equal (1 N each); Earth's huge mass makes its acceleration negligible, not the force.

"Friction from the road is the reaction to the engine's force, so they form a 3rd-law pair on the car."

They act on the same body and are unrelated force types; the true partner of "road pushes tyre forward" is "tyre pushes road backward" on the road. See Normal Force and Friction.

"In tug-of-war the winning team pulls harder on the rope than the losing team."

The rope transmits equal tension both ways; the winner wins by pushing the ground harder, an external force, not by out-pulling the rope pair.

"When you lean on a wall, first you push, then a moment later the wall pushes back."

There is no time delay — the pair is simultaneous; the instant you push, the wall already pushes you.

"A swimmer moves forward because the water's reaction force is the same size as the swimmer's weight."

Weight is a vertical gravitational force with nothing to do with the horizontal swim pair; the swimmer pushes water backward, water pushes swimmer forward — same type, horizontal, unrelated to weight.

"Weight (Earth pulling the book down) and the normal force (table pushing the book up) are a 3rd-law pair because they're equal and opposite."

Wrong — both act on the same body (the book) and are different force types, so it fails the pair test. The genuine pairs are book↔Earth (both gravity) and book↔table (both normal).

Why questions

Why can two equal-and-opposite forces fail to cancel?

Cancellation requires both forces on the same object so they add in that object's net force; a 3rd-law pair splits across two objects, so neither net force sees both. See Free Body Diagrams.

Why does a mosquito splatter on a windscreen while the truck is unharmed, if the forces are equal?

Same force, but

a = F / m

— the mosquito's tiny mass gives it an enormous acceleration and stress, the truck's huge mass barely reacts. See Newton's Second Law.

Why does the lighter of two skaters pushing off fly away faster?

Equal force for equal contact time means equal impulse

F t

, so each gains the same momentum

m Δ v

; hence

m_{A} v_{A} = m_{B} v_{B}

and the smaller mass must take the larger speed.

Why is the third law the reason you cannot lift yourself by pulling your own bootstraps?

Internal action-reaction pairs are equal and opposite and act within the same system, so they contribute zero net external force — only an outside body can accelerate the whole system. See Center of Mass Motion.

Why must we say a pair acts along the same line, not just opposite directions?

If the two equal-opposite forces were offset onto parallel lines, they would tend to spin the system (a turning effect) even with no outside push — but an isolated system can't start spinning on its own, so the pair must share one line.

Why does walking require friction even though your legs supply the force?

Your foot pushes the ground backward (action); the ground pushes you forward (reaction) — without friction the ground can't provide that forward reaction and you'd slip. See Normal Force and Friction.

Edge cases

If two objects are in contact but not moving relative to each other, is there still an action-reaction pair?

Yes — the pair depends on interaction, not motion; static contact still exchanges equal-opposite contact forces.

What is the reaction partner of a force when one "object" is the whole Earth being pulled by a falling ball?

The ball pulling Earth up with equal magnitude; Earth's acceleration is real but astronomically small, so we never notice it.

Two objects interact through empty space via gravity with no contact — do they still obey the third law?

Yes — Newtonian gravity between them is an equal-opposite collinear pair, which is exactly why an isolated two-body system conserves momentum.

Do two charged particles at rest attract/repel with a third-law pair even across empty space?

Yes — the electric forces are equal, opposite, and collinear for static charges, so momentum is conserved just like gravity; only rapidly changing fields carry their own momentum and complicate the simple picture.

In the limit where one mass goes to infinity, does the third law break?

No — the force magnitudes stay equal; only the infinite mass's acceleration goes to zero, so it appears "immovable" while the pair itself is unchanged.

If the contact force between two objects is momentarily zero (they just separate), is there still a pair?

A zero-magnitude force trivially has a zero partner; the pairing statement

F_{A \to B} = - F_{B \to A}

holds with both sides zero, so nothing is violated at the instant of separation.

Does the third law apply between parts of a single rigid body pushing on each other internally?

Yes — internal pairs are equal and opposite and cancel in the body's total, which is precisely why internal forces cannot accelerate the center of mass. See Center of Mass Motion.

Recall One-line self-test

If you can state why each "False" above is false without saying "yes/no," you've internalised the pair. The single sentence that resolves 90% of these traps ::: "A 3rd-law pair acts on two different bodies, so it never cancels and never appears in one free-body diagram."