Newton's First Law | AP Physics 1 Unit 2 Study Guide

Getting Started

This chapter explores the fundamental connection between forces and motion. We will focus on a single object, or a collection of objects defined as a "system," and investigate the precise conditions required for that system's motion to remain unchanged. The core question we will answer is: If an object is moving, does it need a continuous push to keep going, or is there a more fundamental principle at play?

What You Should Be able to Do

After completing this section, you will be able to:

Identify the individual forces acting on a system from its interactions with the environment.
Calculate the vector sum of all forces (the net force) acting on a system.
Define translational equilibrium and identify when a system is in this state.
Use the net force on a system to predict whether its velocity will remain constant or change.
Distinguish between an inertial and a non-inertial reference frame.

Key Concepts & Mechanisms

System & Preconditions

To analyze motion, we first define our system: the object or group of objects we are interested in. Everything outside the system is the environment. The system experiences pushes and pulls, known as forces, due to its interactions with the environment. Our analysis assumes we are observing the system from an Inertial Reference Frame, which is a viewpoint that is not accelerating. An observer standing still on the ground is a good approximation of an inertial frame; an observer in a turning, speeding-up car is not. Newton's laws of motion, as we will study them, are valid only in inertial frames.

Key Steps / Relations

Identify All Force Interactions: A force ( $F$ ), measured in newtons (N), is a vector quantity representing a push or a pull on the system by an object in the environment. To analyze a system, you must first identify every distinct interaction (gravity, contact, tension, etc.) and represent it as a force vector.
Calculate the Net Force: The net force ( $Σ F$ or $F_{n e t}$ ) is the vector sum of all individual forces acting on the system. Because forces are vectors, they must be added according to the rules of vector addition. For forces along a single axis (e.g., the x-axis), this is simple addition and subtraction: $Σ F_{x} = F_{1 x} + F_{2 x} + \dots$ . For forces in two dimensions, you must resolve each force into its x- and y-components and sum the components separately:
- $Σ F_{x} = F_{1 x} + F_{2 x} + \dots$
- $Σ F_{y} = F_{1 y} + F_{2 y} + \dots$
Determine the Equilibrium State: A system is in translational equilibrium if the net force exerted on it is zero. This means the vector sum of all forces is the zero vector.
- $Σ F = 0$
- This implies that for any two perpendicular directions x and y, the sum of the force components along each axis must also be zero: $Σ F_{x} = 0$ and $Σ F_{y} = 0$ . In this state, all forces acting on the system perfectly cancel each other out.

Outputs & Effects

The state of equilibrium directly determines the system's motion. This relationship is defined by Newton's First Law of Motion:

If the net force exerted on a system is zero, the velocity of that system will remain constant.

The velocity ( $v$ ), measured in meters per second (m/s), is a vector describing the rate of change of position. "Constant velocity" means two things:

The object's speed is constant.
The object's direction of motion is constant (it moves in a straight line).

A crucial consequence is that Newton's First Law applies to two distinct scenarios:

Static Equilibrium: The system is at rest and remains at rest ( $v = 0$ ).
Dynamic Equilibrium: The system is moving and continues to move with a constant, non-zero velocity.

Regulation & Limits

The predictive power of Newton's First Law is limited to determining whether velocity is constant or not. It does not describe how the velocity changes when the net force is non-zero; that is the subject of Newton's Second Law. Furthermore, the law's validity is strictly confined to observations made from an inertial reference frame. An observer in an accelerating frame would perceive an object's velocity changing without any apparent net force, a phenomenon that requires the introduction of "fictitious forces" to explain.

Key Models & Diagrams

The primary tool for applying Newton's First Law is the Free-Body Diagram (FBD). This diagram isolates the system and represents all external forces acting on it as arrows originating from a single point. The FBD allows us to translate a physical situation into a mathematical statement about the net force.

Physical Situation	Representation (Free-Body Diagram)	Mathematical Condition & Prediction
A book resting on a horizontal table.	An upward normal force ( $F_{N}$ ) from the table balances the downward gravitational force ( $F_{g}$ ) from the Earth.	$Σ F_{y} = F_{N} - F_{g} = 0$ . Since $Σ F = 0$ , the velocity remains constant (in this case, $v = 0$ ).
A hockey puck gliding on a frictionless ice rink at constant speed.	The upward normal force from the ice balances the downward gravitational force. There are no horizontal forces.	$Σ F_{y} = F_{N} - F_{g} = 0$ . $Σ F_{x} = 0$ . Since $Σ F = 0$ , the velocity remains constant.
A sign hanging from two cables at an angle.	Two upward-and-outward tension forces ( $T_{1}, T_{2}$ ) balance the downward gravitational force ( $F_{g}$ ).	$Σ F_{x} = T_{2 x} - T_{1 x} = 0$ . $Σ F_{y} = T_{1 y} + T_{2 y} - F_{g} = 0$ . Since $Σ F = 0$ , the sign remains at rest.

Key Components & Evidence

Force ( $F$ ): A push or a pull on a system by another object. It is a vector quantity measured in newtons (N).
Net Force ( $Σ F$ ): The vector sum of all forces acting on a system. A non-zero net force causes a change in velocity.
Velocity ( $v$ ): The rate of change of an object's position. It is a vector measured in meters per second (m/s).
Translational Equilibrium: The state of a system where the net force is zero ( $Σ F = 0$ ).
Inertia: The natural tendency of an object to resist changes in its state of motion. Mass is the measure of inertia.
System: The object or collection of objects whose motion is being analyzed.
Inertial Reference Frame: A non-accelerating coordinate system from which observations are made and in which Newton's First Law is valid.
Vector Sum: The process of adding vectors by considering both their magnitude and direction, often by adding their components.
Lab Observation: Objects at rest (like a stapler on a desk) do not spontaneously begin to move, indicating the net force on them is zero.
Lab Observation: A low-friction cart pushed on a track continues to move at a nearly constant velocity long after the push ends, demonstrating that motion does not require a continuous net force.

Skill Snapshots

Causation

An interaction between the system and an external object causes a force to be exerted on the system.
A zero net force causes the system's velocity to be conserved (remain constant).
A non-zero net force causes a change in the system's velocity (an acceleration).

Comparison

Static vs. Dynamic Equilibrium: In static equilibrium, the object's constant velocity is zero. In dynamic equilibrium, the object's constant velocity is non-zero. Both are states of zero net force.
Individual Force vs. Net Force: An object can experience multiple individual forces (like gravity and a normal force) while the net force is zero if the forces are balanced.
Inertial vs. Non-Inertial Frame: An object at rest on a dashboard appears stationary from an inertial frame (the ground). From a non-inertial frame (the accelerating car), it appears to accelerate backward without an applied force.

Change Over Time

Baseline: A system moves with a constant velocity $v_{0}$ . This implies the initial net force on it is zero.
Change 1: A new force is applied, but it is instantly balanced by another force (e.g., increased air resistance). The net force remains zero. The system's velocity continues to be $v_{0}$ .
Change 2: A new, unbalanced force is applied. The net force is now non-zero. The system's velocity will begin to change from $v_{0}$ .
Continuity: As long as the vector sum of all forces on the system remains zero, its velocity will not change.

Common Misconceptions & Clarifications

Misconception: Any object that is moving must have a net force acting on it in the direction of its motion.
- Clarification: A net force is required to change velocity (i.e., to accelerate), not to maintain it. An object moving with constant velocity has zero net force acting on it. The hockey puck gliding on ice is a perfect example.
Misconception: An object in equilibrium must be at rest.
- Clarification: Equilibrium means the net force is zero, which in turn means the velocity is constant. Being at rest ( $v = 0$ ) is just one possible state of constant velocity. A car moving at a steady 60 mph on a straight highway is also in equilibrium.
Misconception: Air resistance or friction are not "real" forces, but just effects that slow things down.
- Clarification: Friction and air resistance are legitimate contact forces that oppose motion or intended motion. In many real-world situations, an applied force is needed to keep an object moving at a constant velocity precisely because that applied force is balancing the force of friction.
Misconception: An object stops moving because it runs out of force.
- Clarification: Objects don't "have" or "contain" force. Forces are interactions. An object that was pushed and is now slowing down is doing so because of an unbalanced net force (usually friction) acting opposite to its motion. Its tendency to keep moving is inertia, not a "force of motion."

One-Paragraph Summary

Newton's First Law of Motion, the law of inertia, establishes the fundamental condition for an object's velocity to remain constant. It states that a system will maintain a constant velocity—which includes being at rest or moving in a straight line at a constant speed—if and only if the net force acting on it is zero. The net force is the vector sum of all individual forces, such as gravity, tension, and friction, that result from the system's interactions with its environment. This state of balanced forces is called translational equilibrium. The law's validity depends on making observations from an inertial (non-accelerating) reference frame, providing the essential baseline for understanding how forces alter motion.

Newton's First Law - AP Physics 1: Algebra-Based Study Guide