Newton's Third Law
For every action there is an equal and opposite reaction. F_A on B = -F_B on A. Forces come in pairs. Explains rockets, walking, and collisions.
Did our AI summary help? Let us know.
Forces always come in pairs F_AB = -F_BA (same magnitude) a = F/m: smaller mass, larger a Rocket: eject mass backward โ thrust forward
Ready to run the numbers?
Why: Third law explains propulsion, contact forces, and why we can walk. Equal forces don't mean equal accelerationsโmass matters. Fundamental to all mechanics.
How: F_action = -F_reaction. Same magnitude, opposite direction. a = F/m so different masses have different accelerations. Momentum conserved: m1v1 + m2v2 = const.
Run the calculator when you are ready.
Input Parameters
Step-by-Step Calculation
Visualizations
For educational and informational purposes only. Verify with a qualified professional.
๐ฌ Physics Facts
Action and reaction act on different bodies
โ HyperPhysics
Walking: push ground back, ground pushes you forward
โ Physics Classroom
Rockets: eject gas backward, gas pushes rocket forward
โ NASA
Collision: forces equal but accelerations differ by mass ratio
โ Khan Academy
๐ Key Takeaways
- โข Action-reaction pairs: Forces always occur in pairs โ when object A exerts a force on object B, object B simultaneously exerts an equal force in the opposite direction on object A
- โข Equal magnitude, opposite direction: The forces are equal in magnitude but opposite in direction โ Fโโ = -Fโโ
- โข Forces on different objects: Action and reaction forces act on DIFFERENT objects, so they cannot cancel each other out โ this is why objects can accelerate despite equal forces
- โข Simultaneous occurrence: Both forces occur at exactly the same instant โ there is no delay between action and reaction
- โข Momentum conservation: The Third Law implies conservation of momentum in isolated systems โ total momentum remains constant
๐ก Did You Know?
๐ฌ How It Works
Newton's Third Law: Fโโ = -Fโโ
Newton's Third Law states that for every action, there is an equal and opposite reaction. This means forces always occur in pairs. When object A exerts a force on object B, object B simultaneously exerts an equal force in the opposite direction on object A. The key insight is that these forces act on DIFFERENT objects, which is why they don't cancel out.
Equal Magnitude
Both forces have exactly the same magnitude. If you push a wall with 100 N, the wall pushes back with 100 N โ not 99 N or 101 N.
Opposite Direction
The forces point in exactly opposite directions. If one force points north, the other points south โ 180ยฐ apart.
Different Objects
Action acts on object B, reaction acts on object A. Since they act on different objects, they cannot cancel โ both objects can accelerate.
Simultaneous
Both forces occur at the exact same instant. There is no delay โ "action" and "reaction" are just names, neither causes the other.
๐ผ Expert Tips
Identify force pairs correctly: True action-reaction pairs always involve the SAME two objects. Weight (Earth-object) and normal force (floor-object) are NOT a pair โ they involve different object pairs.
Remember forces don't cancel: Action and reaction forces act on different objects, so they cannot cancel. Only forces acting on the SAME object can cancel. This is why objects accelerate despite equal forces.
Use F = ma for each object separately: Calculate acceleration for each object using F = ma, where F is the net force ON that object. Larger mass means smaller acceleration for the same force magnitude.
Apply momentum conservation: In isolated systems, the Third Law implies momentum conservation: mโvโ + mโvโ = constant. Use this to solve collision and recoil problems.
๐ Comparison: Newton's Three Laws
| Law | Statement | Formula | Key Concept |
|---|---|---|---|
| First (Inertia) | Object at rest stays at rest; object in motion stays in motion unless acted on by net force | ฮฃF = 0 โ v = const | Inertia |
| Second (F=ma) | Acceleration is proportional to net force and inversely proportional to mass | F = ma | Force causes acceleration |
| Third (Action-Reaction) | Every action has an equal and opposite reaction | Fโโ = -Fโโ | Forces come in pairs |
โ Frequently Asked Questions
If forces are equal, why don't they cancel out?
Action and reaction forces act on DIFFERENT objects, so they can't cancel. Forces only cancel when acting on the SAME object. When you push a wall, you feel the wall push back on you โ but the wall's reaction acts on you, not itself.
Why does only one object move sometimes?
Both objects ALWAYS experience equal forces, but acceleration depends on mass (a = F/m). When you push a car, both you and the car feel equal forces, but the car barely accelerates due to its huge mass, while you might slide backward.
How do rockets work in vacuum (space)?
Rockets don't push against air! They work by the Third Law: the rocket pushes exhaust gases backward, and the gases push the rocket forward. This works perfectly in vacuum โ in fact, it works BETTER without air resistance.
Is there a delay between action and reaction?
No! Action and reaction forces occur simultaneously โ at the exact same instant. There is no cause-and-effect delay. The naming "action" and "reaction" is somewhat misleading; they're really just "interaction pairs."
Why do larger objects exert more force?
They don't! Both objects exert EQUAL forces. The larger object just accelerates less (a = F/m). A small bullet and large gun experience equal forces during firing, but the gun's huge mass means minimal recoil acceleration.
Can action-reaction pairs be different types of forces?
No. Action-reaction pairs are always the SAME type of force. If the action is a contact force, the reaction is also a contact force. If the action is gravitational, the reaction is also gravitational.
How does the Third Law relate to momentum conservation?
The Third Law implies momentum conservation. When two objects interact, their forces are equal and opposite, so the total force on the system is zero. This means total momentum (pโ + pโ) remains constant in isolated systems.
What happens if one object is much more massive?
Both objects still experience equal forces, but the more massive object accelerates much less. For example, Earth pulls you down with your weight, and you pull Earth up with equal force โ but Earth barely moves because its mass is enormous.
๐ Newton's Third Law by the Numbers
๐ Official Sources
โ ๏ธ Disclaimer
This calculator is for educational purposes. Results are approximations based on ideal conditions. Real-world applications may involve friction, air resistance, and other factors not accounted for here. For engineering applications, consult appropriate design standards and safety factors.
Related Calculators
Newton's Second Law Calculator
Calculate force, mass, or acceleration using Newton's Second Law F = ma. Understand the relationship between force, mass, and motion.
PhysicsGravitational Force Calculator
Calculate gravitational force using Newton's Law of Universal Gravitation. Analyze surface gravity, escape velocity, and orbital mechanics.
PhysicsHooke's Law Calculator
Calculate spring force, spring constant, displacement, potential energy, and oscillation using Hooke's Law F = kx.
PhysicsAcceleration Calculator
Calculate acceleration from velocity change, force and mass, or kinematic equations. Analyze g-forces and safety.
PhysicsAngle of Banking Calculator
Calculate ideal banking angle for curves. Analyze speed limits, friction effects, and centripetal force.
PhysicsCar Crash Calculator
Calculate impact forces, g-forces, and injury probability in vehicle collisions. Analyze safety equipment effectiveness.
Physics