Why do forces always occur in pairs, and why does a force pair never cancel?
State Newton's third law, identify action-reaction force pairs, and explain why the two forces in a pair act on different objects and therefore do not cancel.
A Regents Physics answer on Newton's third law: that forces occur in equal and opposite pairs, how to identify an action-reaction pair, why the pair acts on different objects, and why this means the forces never cancel, with worked examples and Reference-Table notes.
Reviewed by: AI editorial process; not yet individually human-reviewed
Have a quick question? Jump to the Q&A page
Jump to a section
What this topic is asking
Newton's third law is the law of force pairs, and the Regents tests it almost entirely conceptually: identifying the reaction to a given force, and explaining why action-reaction pairs do not cancel even though they are equal and opposite. The Physical Setting/Physics course wants you to see that every force is an interaction between two objects, and to use the law to explain propulsion (walking, swimming, rockets) and contact forces.
Newton's third law
The law tells us that forces never occur singly. A hand pushing a wall is matched by the wall pushing the hand; Earth pulling the Moon is matched by the Moon pulling Earth with an equal force. The two forces are always the same type (both gravitational, both contact) and always equal in size, no matter how different the two objects are.
The pair acts on different objects
Consider a small car colliding with a large truck. By the third law, the car pushes on the truck with exactly the same force as the truck pushes on the car. They do not "cancel", because one force acts on the truck and the other on the car. The car accelerates more only because it has less mass (), not because it feels a larger force.
Why force pairs do not cancel
A common confusion is to think the third law forbids any motion, since "every force is balanced". The resolution is that the balance is across two objects. To find whether an object accelerates, you add only the forces acting on that object (its free-body diagram), and a third-law partner of any of those forces acts on a different object, so it is not on this diagram. The horse-and-cart puzzle ("if the cart pulls back as hard as the horse pulls forward, how do they move?") is solved this way: the horse moves because the ground pushes it forward, a separate force from the cart's pull.
Identifying the reaction force
To name the reaction to a given force, swap the two objects and reverse the direction. "Earth pulls the book down (weight)" has the reaction "the book pulls Earth up". "The table pushes the book up (normal force)" has the reaction "the book pushes the table down". A frequent trap is to pair the weight with the normal force: these are both forces on the book, equal and opposite here only by coincidence of equilibrium, and are not a third-law pair (their reactions act on Earth and on the table respectively).
Reference Tables note
Newton's third law is a stated principle and has no equation in the Reference Tables. It underpins the conservation of momentum, treated in conservation of momentum: because the two forces in a collision are equal and opposite and act for the same time, the impulses are equal and opposite, so total momentum is conserved.
Try this
Q1. State Newton's third law. [2 points]
- Cue. When object A exerts a force on object B, B exerts an equal and opposite force on A.
Q2. Explain why an action-reaction pair does not cancel. [2 points]
- Cue. The two forces act on different objects, so each affects only its own object; cancellation needs two forces on the same object.
Exam-style practice questions
Practice questions written in the style of NYSED exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.
Regents (style)1 marksPart A (multiple choice). A book rests on a table. The book pushes down on the table with a force of N. According to Newton's third law, the table pushes on the book with a force of (1) N upward (2) N downward (3) N upward (4) zero. Justify your choice.Show worked answer →
A 1-point Part A item on the third-law pair. The answer is (1).
Newton's third law says the two forces are equal in magnitude and opposite in direction, and act on different objects. The book pushes down on the table with N, so the table pushes up on the book with N. These are the action-reaction pair. (The book's weight is a separate force from Earth, not the reaction to the table's push.)
Regents (style)2 marksPart B-2 (constructed response). A swimmer pushes backward on the water with her hands. Explain, using Newton's third law, how this propels her forward, and identify the two forces in the action-reaction pair.Show worked answer →
A 2-point constructed-response item applying the third law to propulsion.
Force pair (1 point): the swimmer pushes the water backward, and the water pushes the swimmer forward; these are the equal and opposite action-reaction pair.
Explanation (1 point): the forward force from the water acts on the swimmer, providing the net force that accelerates her forward (Newton's second law). Because the two forces act on different objects (one on the water, one on the swimmer), they do not cancel.
Markers reward naming both forces of the pair and stating that the forward force on the swimmer is what propels her.
Related dot points
- State Newton's first law (the law of inertia), relate inertia to mass, and apply the law to objects at rest and moving at constant velocity, recognizing that balanced forces produce no change in motion.
A Regents Physics answer on Newton's first law and inertia: what the law states, how inertia depends on mass, the difference between mass and weight, and how balanced forces leave motion unchanged, with worked examples and Reference-Table notes.
- State and apply Newton's second law, , to calculate net force, mass or acceleration, and analyze situations with several forces by finding the net force first.
A Regents Physics answer on Newton's second law: the relationship between net force, mass and acceleration, why acceleration is proportional to net force and inversely proportional to mass, and how to solve multi-force problems, with worked examples and Reference-Table notes.
- State the law of conservation of momentum, explain it using Newton's third law, and apply it to collisions and explosions where the total momentum before equals the total momentum after.
A Regents Physics answer on conservation of momentum: why total momentum is conserved in an isolated system, how Newton's third law explains it, and how to solve collision and explosion problems with total momentum before equal to total momentum after, with worked examples.
- Draw free-body diagrams showing all forces acting on an object, resolve forces into perpendicular components, and apply the equilibrium condition that the net force is zero in each direction.
A Regents Physics answer on free-body diagrams and equilibrium: how to draw all the forces on an object, resolve them into components, and apply the condition that the net force is zero in each direction for an object at rest or at constant velocity, with worked examples.
- Distinguish mass and weight, calculate weight using , and determine the normal force on an object on a surface, including on a horizontal surface and an incline.
A Regents Physics answer on weight and the normal force: the difference between mass and weight, calculating weight with the Reference-Table equation , and finding the normal force on level ground and on an inclined plane, with worked examples.
Sources & how we know this
- Reference Tables for Physical Setting/Physics — NYSED (2006)
- Physical Setting/Physics Core Curriculum — NYSED (2010)