Unit 2 · Topic 05

Newton's third law

Every interaction between two bodies produces two simultaneous forces, one on each body. Naming both bodies separates the pair from balanced forces.

Unit 2Third lawOpen navigation

Concept 01

Interaction pairs

Essential The minimum you should retain

If A exerts a force on B, B simultaneously exerts a force on A.

UnderstandInterpret and connect

Both forces belong to the same interaction and should be named F_A on B and F_B on A.

DeepenFormulation and conditions

Vectorially, F→A→B=−F→B→A \vec F_{A\to B}=-\vec F_{B\to A} . The minus sign expresses opposite directions in the same coordinate system.

ExploreConnections for further study

The third law traces interactions through a network of bodies without inventing isolated forces.

Mathematical relation

Newton's third-law force pair

F→A→B=−F→B→A \vec F_{A\to B}=-\vec F_{B\to A}
Represents

The two simultaneous forces in one interaction between A and B.

Physical interpretation

They have equal magnitude and opposite directions; they do not cancel in one body's FBD.

DeepenVariables, conditions, and checks

Variables

F⃗_A→B
force exerted by A on B; usual unit: N
F⃗_B→A
force exerted by B on A; usual unit: N

Conditions of application

  • Each force acts on a different body.
  • Both use the same coordinate system.

Dimensional check

Both are measured in N.

Errors it helps prevent

  • Putting the whole pair in one FBD.
  • Inferring equal accelerations.
Two separate bodies receive equal-length forces in opposite directions, each caused by the other body.F_B→AF_A→B

Each arrow is applied to a different body. The forces are simultaneous, equal in magnitude, and opposite in direction.

Concept 02

Equal magnitude and opposite direction

Essential The minimum you should retain

The forces in a pair have equal magnitude and opposite directions, but act on different bodies.

UnderstandInterpret and connect

Equal forces do not imply equal accelerations: each body responds according to its mass and the other forces acting on it.

DeepenFormulation and conditions

Applying the second law separately shows that different accelerations are compatible with the same third-law pair.

ExploreConnections for further study

In a collision, the less massive body usually experiences the greater acceleration magnitude even though the mutual force magnitudes are equal.

Concept 03

Why the pair does not cancel in one FBD

Essential The minimum you should retain

A free-body diagram for one body contains only forces acting on that body. The other member of the pair acts on the other body and does not belong in the same diagram.

UnderstandInterpret and connect

Balanced forces on one body can sum to zero; a third-law pair is distributed across two bodies.

DeepenFormulation and conditions

If both bodies form one system, the pair lies between internal parts and can disappear from the external-force sum.

ExploreConnections for further study

Changing the boundary changes the internal/external classification without removing the physical interaction.

Two bodies appear within a combined boundary, while an individual boundary highlights that only one force of the pair acts on A.system A+Bsystem AB on AA on BAB

With A as the system, only the force of B on A appears. With A+B as the system, the pair is internal and does not enter the external-force sum.

Concept review

Common errors

Each warning includes a concrete way to review the reasoning, not only an incorrect-answer marker.

Drawing both forces of a third-law pair on the same body.

Name agent and receiver: one force acts on A and the other on B.

Cancelling a third-law pair in one body's FBD.

The pair acts on different bodies; it becomes internal only when the system contains both.

Inferring equal accelerations from equal interaction forces.

Apply the second law separately: masses and other forces may differ.