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Action-Reaction
Force Pairs

Master Newton's Third Law by learning to identify and analyze action-reaction force pairs in every physical interaction.

High School Physics

What Is a Force?

A force is a push or pull that one object exerts on another. Forces always arise from interactions between two objects: there is no such thing as a force involving only one object.

Contact Forces
Objects physically touch: friction, normal force, tension, applied push
Field Forces
Objects interact at a distance: gravity, electromagnetic, nuclear

Newton's Third Law

Newton's Third Law states that whenever one object exerts a force on a second object, the second object simultaneously exerts a force equal in magnitude and opposite in direction on the first object.

These two forces are called an action-reaction pair. They always act on different objects, they are always equal in magnitude, and they are always opposite in direction.

Visualizing the Third Law

Hand Wall Action: Hand pushes Wall Reaction: Wall pushes Hand Equal magnitude, opposite direction Each force acts on a different object

Three Key Properties

Equal Magnitude
\(|\vec{F}_{A \to B}| = |\vec{F}_{B \to A}|\) always, regardless of mass or acceleration
Opposite Direction
The two forces point in exactly opposite directions along the same line of action
Different Objects
Each force in the pair acts on a different object: one on A, one on B

The Formal Law

Newton's Third Law For every interaction between objects A and B:
\(\vec{F}_{A \to B} = -\vec{F}_{B \to A}\)
1
Always simultaneous: both forces exist at the same instant, neither causes the other
2
Same type of force: if A pushes B with a contact force, B pushes A with a contact force
3
Cannot cancel: since they act on different objects, they never add to zero on one object

Example: Book on a Table

Table Book Book pushes Table Table pushes Book Action-Reaction Pair 1 (Normal) Earth (below) Earth pulls Book (gravity) Book pulls Earth (gravity)

Balanced Forces vs. Action-Reaction Pairs

Balanced Forces Action-Reaction Pair
Act on Same object Different objects
Direction Opposite Opposite
Magnitude Equal (when balanced) Always equal
Net force Zero on that object Cannot cancel (different objects)
Example Weight + Normal on a book Book pushes Table + Table pushes Book

How to Identify Pairs

1
Pick any force: identify one force and the two objects involved. State it as "A pushes/pulls B."
2
Swap the objects: the reaction is "B pushes/pulls A" with the same type of force.
3
Reverse the direction: the reaction force points in the opposite direction.
4
Check: same magnitude, opposite direction, same force type, different objects. If all four hold, it's a valid pair.

Example 1: Walking

Ground You Foot pushesground back Ground pushesyou forward Action-Reaction: Friction Pair Direction of motion

Example 2: Swimmer Pushing Off a Wall

Pool water Wall Swimmer Feet push wall Wall pushes swimmer Swims away

Example 3: Rocket Propulsion

Rocket Exhaust gas Rocket pushesgas downward Gas pushesrocket upward Action-Reaction Contact Force Pair

Equal Forces, Unequal Accelerations

A common confusion: if the forces are equal, why doesn't the Earth fly up to meet a falling apple? Because acceleration depends on mass.

Apple
\(m = 0.1\,\text{kg}\)
 Earth
\(m = 6 \times 10^{24}\,\text{kg}\)
\(F = 0.98\,\text{N}\)
\(F = 0.98\,\text{N}\)
Same \(|F|\)
\(a = 9.8\,\text{m/s}^2\)
\(a \approx 10^{-25}\,\text{m/s}^2\)

Multiple Pairs in One Scenario

A single situation often contains several action-reaction pairs. Consider a person standing on the floor of an elevator:

Pair 1: Normal
Person pushes floor down; floor pushes person up (contact normal forces)
Pair 2: Gravity
Earth pulls person down; person pulls Earth up (gravitational forces)
Pair 3: Cable
Cable pulls elevator up; elevator pulls cable down (tension forces)

Common Mistakes

✕ Same-Object Pairing
Calling weight and normal force on a book an "action-reaction pair." They act on the same object: not a valid pair.
✕ Unequal Forces Myth
Thinking a truck exerts more force on a car in a collision. The forces are always equal: the car just accelerates more due to less mass.
✕ Mixing Force Types
Pairing a gravitational force with a normal force. Action-reaction pairs must be the same type of force (both gravity or both contact).

Summary Checklist

Criterion Action-Reaction Pair? Not a Pair?
Acts on Two different objects Same object
Direction Opposite Could be any direction
Magnitude Always equal May or may not be equal
Force type Same type Different types
Timing Simultaneous May differ

Question 1 of 5

A book sits at rest on a table. Which pair of forces is a Newton's Third Law action-reaction pair?

Question 2 of 5

A truck and a small car collide head-on. According to Newton's Third Law, the force the truck exerts on the car compared to the force the car exerts on the truck is:

Question 3 of 5

A person is standing still on the ground. The Earth pulls the person downward with gravitational force. What is the reaction force to this?

Question 4 of 5

A rocket accelerates upward by expelling exhaust gas downward. The action-reaction pair is:

Question 5 of 5

Which statement is true about action-reaction force pairs?