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Newton's 3rd law of motion

PhysicsNewtonian mechanicsForcesMomentum

Summary

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. This is the key point the MCAT tests.

Detail

Meaning: Forces come in interaction pairs. If A pushes on B with force F, then B pushes on A with force −F. The pair has the same magnitude, opposite directions, the same type of force (both gravitational, both normal, both frictional), and acts along the same line. Because each force acts on a different object, the two do not add together in a free-body diagram of either one.

Equation: FAB = −FBA, where FAB is the force on A due to B and FBA is the force on B due to A, both in newtons (N).

On the MCAT: Typical questions ask about a collision, a recoiling gun, a rocket, or a person pushing on a wall or the floor. Equal forces do not mean equal accelerations. Since a = F/m, the less massive object accelerates more. Third-law pairs also underlie momentum conservation: equal and opposite forces act for the same time, so the impulses are equal and opposite. Expect questions about the reaction partner of a given force.

Common confusion: Students think the pair cancels, so nothing could ever accelerate. Cancellation only happens between forces on the same object. Another trap is treating weight and the normal force on a book at rest as a third-law pair. They are not. Both act on the book, and they balance by the first law. The partner of Earth's pull on the book is the book's pull on Earth.

Sources

  • Physics (Cutnell and Johnson)
  • Physics (Giancoli)
  • University Physics (Young and Freedman)

Written for the MCAT and checked before it was published. For study reference only. Spotted an error? Let us know.