Newton's Third Law and Free-Body Diagrams

AP Physics 1· AP Physics 1 CED — Dynamics· 14 min read

1. Newton's Third Law and Action-Reaction Pairs★★☆☆☆⏱ 4 min

Newton's third law (N3L) describes the interaction force between any two objects: whenever object A exerts a force on object B, object B exerts an equal-magnitude, opposite-direction force of the same type back on object A. This is a foundational rule for all dynamics problems on the AP Physics 1 exam.

\vec{F}_{A \text{ on } B} = - \vec{F}_{B \text{ on } A}

📘 Definition

Action-Reaction Pair

A pair of interaction forces described by Newton's third law, with three mandatory tested properties

Example:

Earth pulling on a book, and book pulling on Earth (both gravitational)

Always act on two different objects (never the same object)
Always the same type of force (e.g., gravitational, normal, frictional)
Equal in magnitude at all times, even if objects accelerate or have different masses

📐 Worked Example

A 60 kg astronaut pushes off a 120 kg stationary space capsule in deep space (no gravity or air resistance). Immediately after they lose contact, what is the relationship between the magnitude of the force the astronaut exerts on the capsule ( $F_{A o n C}$ ) and the magnitude of the force the capsule exerts on the astronaut ( $F_{C o n A}$ )?

A. $F_{A o n C} = F_{C o n A}$
B. $F_{A o n C} > F_{C o n A}$ because the capsule has more mass
C. $F_{A o n C} < F_{C o n A}$ because the astronaut will accelerate more
D. There is not enough information to determine the relationship

1
The interaction between the astronaut and capsule is a contact force interaction, so Newton's third law applies directly to the force pair between them.
2
Newton's third law requires that interaction force pairs are always equal in magnitude, regardless of the masses or accelerations of the two objects.
3
The different accelerations of the astronaut and capsule are explained by Newton's second law $a = F_{n e t} / m$ : same magnitude force, different masses give different accelerations, but this does not change the equal magnitude of the interaction force pair.
4
The only correct option is A.

Exam tip:

On any question asking you to identify an action-reaction pair, first eliminate any pair that acts on the same object — that is never a Newton's third law pair.

2. Drawing Correct Free-Body Diagrams★★☆☆☆⏱ 4 min

🚫 No Calculator

A free-body diagram (FBD) is a standardized graphical tool to isolate all forces acting on a single target object or system, so you can correctly apply Newton's second law. The AP Physics 1 exam regularly awards points for correct force direction, correct labeling, and excluding invalid forces.

Represent the target object as a single point (all forces act on the center of mass for rigid bodies)
Draw each force vector starting at the point, pointing outward in the direction the force acts
Label every force with a standard label indicating type and source
Never include net force, or forces the target object exerts on other objects

📐 Worked Example

A 5 kg block is sliding upward along a rough inclined plane (no external push acts on the block after it was set in motion). Draw a correct free-body diagram for the block, and list all forces with their sources.

1
Define the system as the 5 kg block, our target object of interest.
2
Identify all non-contact forces acting on the block: gravitational force from Earth, pointing vertically downward, labeled $F_{g}$ .
3
Identify all contact forces: the block only touches the incline, which exerts two forces: (a) normal force perpendicular to the incline surface, pointing outward toward the block, labeled $F_{N}$ ; (b) kinetic friction parallel to the incline, opposing the block's upward motion, so it points down the incline, labeled $f$ .
4
No other forces act on the block: the 'force of motion' pushing it upward is a fictitious force with no identifiable source, so it is not included. The final FBD has three correctly directed and labeled vectors, no extra forces.

Exam tip:

If you are ever tempted to draw a 'force of motion' or 'force of inertia' on an FBD, stop: all forces must come from an interaction with another object, so these fictitious forces are never allowed, and including them will lose points.

3. Internal vs. External Forces and System Selection★★★☆☆⏱ 4 min

When solving problems involving multiple interacting objects, you can choose to treat each object as a separate system or treat multiple objects together as a single combined system. This choice is valid because of Newton's third law, and it drastically simplifies calculations for connected objects.

📘 Definition

Internal Force

A force that acts between two objects that are both inside the defined system. Per Newton's third law, internal forces form equal and opposite action-reaction pairs that sum to zero, so they can be ignored when calculating net force for the whole system.

📘 Definition

External Force

A force exerted by an object outside the defined system on an object inside the system. Only external forces contribute to the net force of the entire system.

This method lets you find the acceleration of the entire system first, without solving for internal forces like tension first. You can then go back and solve for internal forces after you know the acceleration.

📐 Worked Example

Two blocks of mass $m_{1} = 2 kg$ and $m_{2} = 3 kg$ are connected by a massless string on a frictionless horizontal table. A horizontal applied force $F = 10 N$ pulls on $m_{1}$ to the right. What is the acceleration of the two-block system?

1
Choose the system to be both blocks together, so total mass $M = m_{1} + m_{2} = 2 kg + 3 kg = 5 kg$ .
2
Classify forces: the tension between the blocks is internal to the system, so per Newton's third law, the tension force on $m_{1}$ and the tension force on $m_{2}$ cancel out, so we ignore them.
3
Vertically, weight and normal force from the table balance to zero. The only net external horizontal force on the system is the applied force $F = 10 N$ .
4
$a = \frac{F_{net}}{M} = \frac{10\ \text{N}}{5\ \text{kg}} = 2\ \text{m/s}^2$
5
The acceleration of the system is $2 m/s^{2}$ to the right, matching the result of solving for each block separately but much faster.

Exam tip:

If an FRQ asks for the acceleration of a system of multiple connected objects, always use the combined system method first to get acceleration quickly, then solve for internal forces separately.

4. AP-Style Concept Check★★★☆☆⏱ 2 min

✓ Quick check

Test your understanding of core N3L and FBD concepts with this AP-style multiple choice question:

A student places a full coffee mug on a horizontal wooden desk, which sits on the classroom floor. Which of the following options correctly identifies a Newton's third law action-reaction pair in this scenario?
- The gravitational force of Earth on the mug, and the normal force of the desk on the mug
- The gravitational force of Earth on the mug, and the gravitational force of the mug on Earth
- The normal force of the desk on the mug, and the weight of the mug
- The gravitational force of the mug on the desk, and the normal force of the desk on the mug
Reveal answer
1 —
Correct. This pair meets both N3L rules: same force type (gravitational) and acts on two different objects. All other options fail at least one rule.

5. Common Pitfalls

Wrong move:

Labeling the normal force on a resting book and the weight of the book as an action-reaction pair.

Why:

Students confuse balanced forces (two forces on the same object that sum to zero) with Newton's third law pairs, which always act on two different objects.

Correct move:

For any candidate N3L pair, check what each force acts on: if both act on the same object, it cannot be an N3L pair, and confirm both are the same type of force.

Wrong move:

Drawing the normal force on an incline pointing straight upward instead of perpendicular to the incline surface.

Why:

Students confuse normal force direction with the direction of weight, or assume normal force always opposes gravity.

Correct move:

Normal force is always perpendicular to the contact surface between two objects, so point it perpendicular to the surface, regardless of gravity's direction.

Wrong move:

Including a 'force of motion' on an FBD for a sliding object.

Why:

Students intuitively think moving objects need a force to keep them moving, from everyday experience with friction, leading to this misconception.

Correct move:

Every force on an FBD must come from an interaction with an identifiable object outside the system; if you can't name the source object, the force doesn't exist.

Wrong move:

Including internal forces in the net force calculation for a combined system.

Why:

Students forget internal forces cancel per Newton's third law, leading to under or over-counting net force and wrong acceleration.

Correct move:

When drawing an FBD for a combined system, cross out any force that acts between two objects inside the system before calculating net force.

Wrong move:

Claiming action-reaction forces cancel out when calculating acceleration of a single object.

Why:

Students remember 'equal and opposite' so they assume the forces sum to zero, leading to a wrong conclusion of zero acceleration.

Correct move:

Action-reaction forces act on different objects, so you only include one of the two forces in the FBD of your target object, so they never cancel in the $F_{n e t}$ for that object.

6. Quick Reference Cheatsheet

Category	Rule / Formula	Notes
Newton's Third Law	$F_{A on B} = - F_{B on A}$	Equal magnitude, opposite direction, two different objects, same force type
Action-Reaction Check	Two different objects; 2. Same force type	Eliminate wrong answers on AP exams with this check
FBD Core Rule	Only forces on target system included	Never add fictitious forces or forces on other objects
Normal Force Direction	Always perpendicular to contact surface	Never automatically draw straight up unless surface is horizontal
Friction Force Direction	Parallel to contact, opposes relative motion	Friction can act in the direction of an object's motion
Internal Forces (Combined System)	Internal forces cancel per N3L	Ignore internal forces when calculating system acceleration
Net Force on FBD	Sum external forces to get $F_{n e t}$	Never add $F_{n e t}$ as an extra force to the FBD

When this came up on past exams

AI-estimated based on syllabus patterns — cross-check with official past papers for accuracy. Use only as revision-focus signals.

2023 · MCQ
Identify valid action-reaction pair
2022 · FRQ
Draw FBD for connected objects
2021 · MCQ
Compare N3L force magnitudes

What's Next

Mastering Newton's third law and free-body diagrams is the critical foundation for all subsequent dynamics topics in AP Physics 1. Every problem involving forces, from incline planes to circular motion to collisions, requires you to correctly identify forces and draw valid FBDs as the first step. Mistakes in this step will propagate to incorrect answers even if you apply Newton's second law correctly, so it is essential to master these conventions before moving on to more complex problems. Next, you will apply these core skills to solve applied dynamics problems that are heavily tested on the AP Physics 1 exam.