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Newton's First Law
The Law of Inertia

Understand why objects at rest stay at rest and objects in motion keep moving: the foundational principle of inertia and net force.

AP Physics 1

What Is Inertia?

Inertia is the natural tendency of an object to resist changes in its state of motion. An object at rest wants to stay at rest, and an object moving at constant velocity wants to keep moving at that velocity.

Understanding Net Force

The net force on an object is the vector sum of all forces acting on it. When we write \(\vec{F}_{\text{net}}\), we mean the single force that would produce the same effect as all forces combined.

\(m\)
\(F_1 = 20 \text{ N}\)
\(F_2 = 8 \text{ N}\)
\(F_{\text{net}} = 12 \text{ N}\)

Why Does Newton's First Law Matter?

Foundation
It defines what happens when forces are balanced: the default state of motion is constant velocity, not rest.
Everyday Physics
Seat belts, airbags, and anti-lock brakes all exist because of inertia: your body keeps moving when the car stops.
Problem Solving
If \(\vec{F}_{\text{net}} = 0\), you immediately know \(\vec{a} = 0\). This simplifies countless AP Physics problems.

The Formal Statement

Mathematically, Newton's First Law states:

The converse is equally important: if an object's velocity is changing, there must be a nonzero net force acting on it.

Equilibrium in a Free-Body Diagram

\(m\)
\(N\)
\(mg\)
\(f\)
\(F\)

Two Cases of First Law

Case 1: At Rest
A book on a table: \(\vec{v} = 0\), \(\sum \vec{F} = 0\). Normal force balances gravity. The book stays put.
Case 2: Constant Velocity
A puck on frictionless ice: \(\vec{v} = \text{const}\), \(\sum \vec{F} = 0\). No force needed to maintain motion.

Inertia vs. Force

Inertia Force
Definition Resistance to change in motion A push or pull on an object
Depends on Mass only Interaction between objects
Units kg (measured by mass) Newtons (N)
Vector? No (scalar property) Yes (magnitude + direction)
Role in 1st Law Why objects resist acceleration What causes acceleration

How to Apply Newton's First Law

1
Identify the object. Choose the single object whose motion you are analyzing.
2
Draw a free-body diagram. Sketch every external force acting on the object (gravity, normal, friction, tension, applied).
3
Determine the net force. Add all force vectors: \(\vec{F}_{\text{net}} = \sum \vec{F}\).
4
Apply the First Law. If \(\vec{F}_{\text{net}} = 0\), then \(\vec{a} = 0\) and velocity is constant. If not, a net force is causing acceleration.

Example 1: Book on a Table

\(2 \text{ kg}\)
\(mg = 19.6 \text{ N}\)
\(N = 19.6 \text{ N}\)

Example 2: Constant Velocity Car

A car travels at a steady \(25 \text{ m/s}\) on a straight highway. The engine provides a forward force of \(3000 \text{ N}\). What is the total resistive force (air drag + friction)?

\(v = 25 \text{ m/s}\)
\(3000 \text{ N}\)
\(f_{\text{resist}}\)
constant \(\vec{v}\)

Example 3: Hanging Sign in Equilibrium

A \(15 \text{ kg}\) sign hangs from two cables making angles of \(30^\circ\) and \(45^\circ\) with the horizontal. Find the tension in each cable.

\(15 \text{ kg}\)
\(30^\circ\)
\(45^\circ\)
\(T_1\)
\(T_2\)
\(147 \text{ N}\)

Inertial Reference Frames

Newton's First Law only holds in an inertial reference frame: a frame of reference that is not accelerating. If your frame accelerates, "fictitious forces" appear.

Inertial Frame
A lab on solid ground, a train at constant velocity. Newton's laws apply directly.
Non-Inertial Frame
A braking car, a spinning ride. Objects appear to accelerate without a real force.

First Law vs. Second Law

First Law Second Law
Condition \(\sum \vec{F} = 0\) \(\sum \vec{F} \neq 0\)
Result \(\vec{a} = 0\), constant \(\vec{v}\) \(\vec{a} = \frac{\sum \vec{F}}{m}\)
Tells us What happens with no net force How much acceleration a net force causes
Key use Equilibrium problems Dynamics problems

Common Mistakes

✕ "Motion requires force"
Many students think a moving object needs a force to keep moving. In reality, no net force is needed to maintain constant velocity.
✕ "Heavier = slower"
Greater mass means more inertia, but it does not mean the object moves slower. It means it is harder to change its velocity.
✕ Forgetting friction
On Earth, friction and air drag are always present. Objects slow down because of these forces, not because "force runs out."

Question 1 of 5

A hockey puck slides across frictionless ice at a constant speed of \(5 \text{ m/s}\). What is the net force acting on the puck?

Question 2 of 5

An astronaut floating in the International Space Station releases a ball. In the station's reference frame, the ball:

Question 3 of 5

A box sits at rest on a rough floor. A person pushes it with a horizontal force of \(40 \text{ N}\), but it does not move. What can you conclude about the friction force?

Question 4 of 5

Which of the following is an example of Newton's First Law in action?

Question 5 of 5

A skydiver reaches terminal velocity and falls at a constant \(55\) m/s. At terminal velocity, the net force on the skydiver is: