AP Physics 1  ·  Unit 2: Forces & Translational Dynamics  ·  Lesson 2.4

Deep Dive: Newton's First Law

🔬 Deep Dive
This is your textbook for this topic. Take your time. Read it more than once.
2.4.A.1Concept⚠ Watch Out

Inertia

Inertia is a property of matter — specifically, its tendency to resist any change in velocity. An object with more mass has more inertia. It takes more force to get it moving, more force to stop it, and more force to change its direction.

2 kg10 kgF = 20 NF = 20 Na = 10 m/s²a = 2 m/s²Same force — very different accelerations. Mass is inertia.
⚠️Inertia is not a force. Students often write things like "the ball keeps moving because of inertia" as if inertia is pushing it forward. Inertia is a resistance to change, not a cause of motion. Nothing keeps the ball moving — the absence of a net force just means its velocity doesn't change.

In AP Physics 1, inertia is measured by mass. A 10 kg block has five times the inertia of a 2 kg block — meaning the same force produces one-fifth the acceleration. That's exactly what Newton's Second Law quantifies: a = ΣF / m.

2.4.A.2Concept

Newton's First Law — Stated Precisely

If the net external force on a system is zero, the velocity of that system's center of mass remains constant. That's the whole law. Two scenarios both satisfy it:

At rest (v = 0)

A book sitting on a table. Net force is zero — normal force balances gravity. The book stays put because nothing is changing its velocity from zero.

Constant velocity (v ≠ 0)

A hockey puck gliding on frictionless ice. Net force is zero — nothing is pushing or slowing it. It keeps moving at the same speed in the same direction indefinitely.

🔑This is the conceptual test graders use on FRQs: if a student explains constant-velocity motion by saying "the forces balance," that's incomplete. A full credit answer invokes Newton's First Law by name and states that a zero net force means no change in velocity.
2.4.A.3ConceptMath

Translational Equilibrium

Translational equilibrium is the condition where the vector sum of all forces on a system equals zero. The system is not necessarily at rest — it could be moving at constant velocity. The defining equation is:

ΣF⃗ᵢ = 0

This means every force in one direction is perfectly cancelled by forces in the opposite direction. The net force vector — when you add all the individual force vectors together — points nowhere, because they all cancel.

30 N30 N20 N20 NΣF = 0 → v = constant
ExampleWorked Example — Is This Object in Equilibrium?

A 5 kg lamp hangs from the ceiling by a single cable. The lamp is at rest. Find the tension in the cable and state whether the system is in translational equilibrium.

2.4.A.4Concept⚠ Watch Out

Applying the First Law Per Axis

The First Law applies independently in each dimension. A system can be in equilibrium horizontally — constant vₓ — while simultaneously accelerating vertically. The two axes don't talk to each other.

⚠️The most common mistake: assuming that if forces are balanced in one direction, the object must be in equilibrium overall. A projectile at the peak of its arc has zero vertical velocity — but gravity is still acting vertically, so it's accelerating downward. Horizontally, there's no force, so vₓ stays constant. That's two different situations in two directions at the same time.

Adjust forces in each direction independently. Notice how a system can be in equilibrium in one direction while accelerating in another.

→ Right15 N
← Left15 N
↑ Up30 N
↓ Down20 N
Horizontal (x)
ΣFₓ = 0 → vₓ stays constant
✓ First Law applies — constant velocity
Vertical (y)
ΣFᵧ = +10 N → accelerating up
⚡ Second Law applies — accelerating
ExampleGuided Example — Equilibrium in One Direction, Not the Other

A 3 kg block is pushed horizontally at constant velocity across a rough floor while gravity and the normal force act vertically. Show that Newton's First Law applies in both directions, but for different reasons.

Step 1Set up the free-body diagram
Four forces: applied force F_app to the right, friction f_k to the left, normal force F_N upward, gravity F_g = 30 N downward.
2.4.A.5Concept

Inertial Reference Frames

Newton's First Law only works when you observe it from an inertial reference frame — a frame that is itself not accelerating. In an inertial frame, an object with no net force truly moves at constant velocity (or stays at rest). If your frame is accelerating, you'll see objects appear to accelerate for no reason, which violates the First Law.

💡You met inertial reference frames back in Lesson 1.4. The connection now: Newton's First Law is the definition of an inertial frame. If you're in a frame where the First Law holds — objects with no net force move at constant velocity — then your frame is inertial.

The classic non-inertial example: a passenger in a braking car feels themselves thrown forward, even though nothing is pushing them. From outside (inertial frame), the car decelerated but the passenger's inertia kept them moving forward — no mystery. From inside the braking car (non-inertial frame), it looks like an invisible force pushed them, which is why Newton's First Law seems to break down.

🔑For all AP Physics 1 problems, assume an inertial reference frame unless explicitly told otherwise. The surface of the Earth is treated as approximately inertial for all problems in this course.
← Back to Lesson 2.4Next: Lesson 2.5 →Newton's Second Law — the one equation that runs the whole unit.
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