Interactions, Forces, and Newton's Laws

Driving question

How do interactions change the motion of a chosen system?

Hook: why does the passenger lean?

A bus accelerates forward and a standing passenger appears to lean backward. No mysterious backward force is needed. The passenger's body tends to retain its velocity while the floor exerts a forward friction force on the feet. The observation becomes clear once we choose a system and identify forces on it.

Dynamics connects interactions to changes in motion. Its core reasoning chain is:

choose a system → identify external interactions → draw forces → add vectors → predict acceleration.

Force is an interaction

A force is a push or pull exerted by one object on another. Name it with two objects: $\vec F_{A\text{ on }B}$ means “force exerted by $A$ on $B$.” Force is measured in newtons, where

Common interactions include gravitational force, normal force, tension, friction, drag, and applied contact forces. Velocity and acceleration are not forces.

Free-body diagrams

A free-body diagram isolates one chosen object or system and shows only external forces acting on it.

1. Draw the system as a dot or simple box.
2. Draw one arrow for each external force, beginning at the system.
3. Label each arrow by force type or by agent and receiver.
4. Choose axes that simplify components.
5. Do not add velocity, acceleration, or forces exerted by the system.

For a book resting on a level table, Earth pulls downward with $F_g=mg$ and the table pushes upward with $F_N$. If vertical acceleration is zero, these forces balance. The normal force is not automatically equal to weight; that equality follows only from the vertical force equation in this specific situation.

Newton's first law: zero net force

In an inertial reference frame, an object with zero net external force maintains constant velocity:

Constant velocity includes rest. Motion does not require a continuing net force. A sliding object commonly stops because friction provides a net force opposite its motion.

Newton's second law: net force predicts acceleration

For constant mass,

This vector equation becomes a component equation for each axis:

Acceleration points in the direction of the net force, not necessarily in the direction of velocity.

Worked example: delivery crate

A $12.0\text{ kg}$ crate is pulled horizontally right with $50.0\text{ N}$. Kinetic friction is $14.0\text{ N}$ left. Find its acceleration.

Choose right as positive. Vertically, $F_N-mg=0$. Horizontally,

so

The applied force is not $ma$; the net force, $36.0\text{ N}$, is $ma$.

Newton's third law: one interaction, two forces

If object $A$ exerts a force on object $B$, then $B$ simultaneously exerts an equal-magnitude, opposite-direction force on $A$:

The pair never cancels on one free-body diagram because the two forces act on different objects. The book's weight and the table's normal force both act on the book, so they are not a third-law pair. The third-law partner of the table's force on the book is the book's force on the table.

Friction and contact models

Static friction adjusts up to a maximum:

When surfaces slide, a useful model is

Static friction is not always $\mu_sF_N$; it reaches that value only at impending slip. Friction opposes relative slipping or the tendency to slip, not always the object's velocity.

Incline reasoning

For a block on an incline of angle $\theta$, choose axes parallel and perpendicular to the surface. Weight components are

If nothing else accelerates the block perpendicular to the surface, $F_N=mg\cos\theta$. Components are bookkeeping tools; the gravitational force remains one downward vector.

Connected systems

Two carts connected by a light string share an acceleration magnitude while the string is taut. You may analyze each cart separately to find tension, or treat both carts as one system so their mutual tension forces are internal and cancel from the system equation.

Original example: A $2.0\text{ kg}$ cart and a $3.0\text{ kg}$ cart move together on a nearly frictionless track. A horizontal $15\text{ N}$ force pulls the $3.0\text{ kg}$ cart.

For both carts,

For the $2.0\text{ kg}$ cart alone, tension is the only horizontal force:

AP-style evidence routine

1. State the system and interval.
2. Identify every external interaction.
3. Draw a free-body diagram before writing equations.
4. Choose axes and resolve only the vectors that need components.
5. Write $\sum F=ma$ separately for each axis.
6. Solve symbolically, then substitute values with units.
7. Check direction, dimensions, limiting cases, and whether the model assumptions hold.

Misconception clinic

“Moving forward means a forward net force.” Forward velocity can coexist with zero or backward net force.

“Action and reaction cancel.” They act on different objects. Only forces on the same chosen system can cancel in its net force.

“Normal force always equals weight.” It depends on all perpendicular forces and perpendicular acceleration.

“Static friction is always $\mu_sF_N$.” It adjusts from zero to a maximum.

Retrieval pause

1. What belongs on a free-body diagram?
2. Can an object move with zero net force? Explain.
3. Why are weight and normal force not a third-law pair?
4. When is $F_N=mg$ valid?
5. Why can treating connected carts as one system simplify the equation?

Key takeaway

Newton's laws become reliable when forces are treated as interactions and the system boundary is explicit. A correct free-body diagram is not decoration—it is the evidence map from which the equations follow.

Further learning and alignment

• College Board, “AP Physics 1: Algebra-Based Course,” https://apcentral.collegeboard.org/courses/ap-physics-1 (retrieved 2026-08-18). Standards and course-alignment reference only; no endorsement implied.
• OpenStax, “4.1 Force” and “4.4 Newton's Third Law of Motion,” https://openstax.org/books/physics/pages/4-1-force and https://openstax.org/books/physics/pages/4-4-newtons-third-law-of-motion (retrieved 2026-08-18). CC BY; used for concept verification, not copied exercises.
• NASA Glenn Research Center, “Newton's Laws of Motion,” https://www1.grc.nasa.gov/beginners-guide-to-aeronautics/newtons-laws-of-motion/ (retrieved 2026-08-18). U.S. government educational reference; used to verify concise law summaries.