AP Physics C: Mechanics · Unit 2: Force and 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.12.4.A.2ConceptMath

Net Force and Translational Equilibrium

The net force on a system is simply the vector sum of every individual force exerted on it — exactly what your free-body diagram from Lesson 2.2 already shows you, added together.

When that vector sum comes out to exactly zero, the system is said to be in translational equilibrium:

ΣF⃗ᵢ = 0

Try building your own force system below — three adjustable forces, shown both from a free-body-style common origin and as a tip-to-tail vector chain. When the chain closes back on itself, the system is in equilibrium.

Adjust three forces acting on a system. The left diagram shows them from a common origin (like a free-body diagram); the right shows the same vectors added tip-to-tail. If the chain closes back to its starting point, the system is in equilibrium.

F1 = 8 N
θ1 = 30°
F2 = 8 N
θ2 = 150°
F3 = 6 N
θ3 = 270°
From the dot (FBD-style)Tip-to-tail sum
✕ ΣF⃗ ≠ 0 — net force ≈ 2.0 N. This system's velocity will change.
2.4.A.3Concept

Newton's First Law

Newton's first law states that if the net force exerted on a system is zero, the system's velocity will remain constant.

ΣF⃗ = 0  ⟹  v⃗ = constant
⚠️"Constant velocity" includes zero velocity — a system at rest stays at rest — but it just as validly includes any nonzero constant speed in a straight line. Don't read "equilibrium" as a synonym for "not moving." A hockey puck sliding across frictionless ice at a steady 5 m/s is in exactly as much equilibrium as one sitting still.
2.4.A.4Concept

Balanced in One Direction, Unbalanced in Another

Equilibrium is checked axis by axis, not just as a single overall yes-or-no. Forces can be perfectly balanced along one direction while completely unbalanced along a perpendicular direction — and a system's velocity will change only along the unbalanced direction, staying constant along the balanced one.

🔑This is exactly why a block sliding across a table under an applied horizontal force can have zero vertical acceleration (normal force balances gravity) while accelerating horizontally the entire time (applied force exceeds friction). Two independent axes, two independent verdicts.

Try it directly below, using the same block-on-track scenario from Lesson 2.2's free-body diagram tool.

The block-on-track scenario from Lesson 2.2. Adjust the four forces — watch how the two axes are judged completely independently.

N (up)20
mg (down)20
F(app) (right)6
f(k) (left)3
Vertical axis
N − mg = 0 N
Balanced — no vertical acceleration.
Horizontal axis
F(app) − f(k) = 3 N
Unbalanced — block accelerates horizontally.

Try setting the sliders so one axis is balanced and the other isn't — this is exactly the situation described in 2.4.A.4.

ExampleGuided Example — Constant Velocity on an Incline

A block slides down a rough incline at a constant velocity. What does this tell you about the net force on the block, both along the incline and perpendicular to it?

Step 1Recall what constant velocity means
By Newton's first law, constant velocity — even nonzero, even while moving — means the net force on the block is zero.
2.4.A.5Concept

Inertial Reference Frames

An inertial reference frame is one from which an observer would actually verify Newton's first law — a frame where objects with zero net force genuinely appear to move at constant velocity, rather than mysteriously accelerating for no apparent reason.

💡This connects directly back to Lesson 1.4: acceleration is the same in every inertial frame, which is exactly why Newton's first law holds consistently in all of them. An accelerating frame (like a braking car) is non-inertial — objects inside it can appear to accelerate even with zero real force acting on them, purely because the frame itself is accelerating.

Unless a problem explicitly states otherwise, you may assume every reference frame in this course is inertial — the same boundary assumption introduced back in Lesson 1.4.

← Back to Lesson 2.4Ready for 2.5? Newton's Second Law is what happens the moment ΣF⃗ stops being zero.