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Set up the interaction

Tip: Most students confuse “action–reaction” with “balanced forces.” This tool prevents that.

We’ll label forces as F(A→B) and F(B→A).

Angle measured from +x axis. Example: 0° = right, 90° = up, 180° = left.

Options:

Chips prefill the form and run the calculation.

Result:

No results yet. Choose a mode and click Calculate.

How to use this calculator

  • Pick a mode: Basic, Scenario, or Insight.
  • Enter objects: who interacts (A and B).
  • Provide a force (optional in Scenario mode) and click Calculate.
  • Read the pair: F(A→B) and F(B→A) — equal magnitude, opposite direction.

How this calculator works

  • Third-Law pair: if A pushes B, then B pushes A back.
  • Equal magnitude: |F(A→B)| = |F(B→A)|
  • Opposite direction: θ(B→A) = θ(A→B) + 180°
  • Key point: they act on different objects, so they don’t cancel on one free-body diagram.

Formula & Equations Used

Newton’s Third Law: F(A→B) = −F(B→A)

Angle flip: θ₂ = (θ₁ + 180°) mod 360°

Components (optional): Fₓ = F cosθ, Fᵧ = F sinθ

Insight mode: a = F / m (same F, different m ⇒ different a)

Example Problems & Step-by-Step Solutions

Example 1 — Skater A pushes Skater B with 120 N left

If A exerts 120 N on B to the left, then B exerts 120 N on A to the right. Equal magnitude, opposite direction, different objects.

Example 2 — Book and table (normal force)

The table pushes up on the book (normal). The book pushes down on the table with the same magnitude. That’s the action–reaction pair.

Example 3 — Same force, different accelerations

Two carts interact with the same 50 N force. If one cart has 2 kg and the other has 10 kg: a(2 kg)=25 m/s² and a(10 kg)=5 m/s². Same interaction force, different outcomes due to mass.

Frequently Asked Questions

Q: Do action–reaction forces cancel?

Not on a single object. They act on different objects, so they don’t cancel on one free-body diagram.

Q: Is “equal and opposite” the same as equilibrium?

No. Equilibrium means the net force on one object is zero. Third-law pairs are across two objects.

Q: Can the forces be different if masses differ?

The interaction forces are equal in magnitude. Different masses cause different accelerations via a = F/m.

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