Unit 2 · Topic 02

Newton's first law

The first law rejects the idea that motion requires a forward net force: a net force is required to change velocity.

Unit 2First lawOpen navigation

Concept 01

Inertia

Essential The minimum you should retain

If net force is zero, a body preserves its velocity vector. Rest and uniform straight-line motion are two cases of the same principle.

UnderstandInterpret and connect

Inertia is resistance to changing velocity, not a force that pushes the body. Everyday friction can hide this idea by slowing objects.

DeepenFormulation and conditions

Constant velocity includes constant magnitude and direction; a curved path has acceleration even when speed stays constant.

ExploreConnections for further study

Imagining an environment with negligible interactions separates natural motion from the effect of external forces.

x(t) at constant velocity

Linear position-time graph for an object with constant positive velocity.
  • x(t)=2t

The line has constant slope: the object changes position without acceleration or net force.

Concept 02

Zero net force

Essential The minimum you should retain

ΣF→=0 \sum\vec F=0 implies a = 0 and therefore a constant velocity vector. It does not necessarily imply rest.

UnderstandInterpret and connect

The sum can be zero because no forces act or because several forces on the same body balance.

DeepenFormulation and conditions

The vector condition requires zero in every independent component. One unbalanced component is enough to produce acceleration.

ExploreConnections for further study

Translational equilibrium follows from zero net force, but its systematic applications belong to Unit 3.

Mathematical relation

First law in an inertial frame

ΣF→=0→⇒a→=0→⇒v→=constante \sum\vec F=0\Rightarrow\vec a=0\Rightarrow\vec v=\mathrm{constante}
Represents

Preservation of the velocity vector when net force is zero.

Physical interpretation

This includes both rest and uniform straight-line motion.

DeepenVariables, conditions, and checks

Variables

ΣF⃗
net force; usual unit: N
a⃗
acceleration; usual unit: ms² m/s^2
v⃗
velocity; usual unit: m/s

Conditions of application

  • The description uses an inertial frame.

Dimensional check

Each equality compares quantities of the same kind.

Errors it helps prevent

  • Concluding that velocity must be zero.
  • Concluding that no forces act.

Concept 03

First law and reference frames

Essential The minimum you should retain

The first law identifies inertial frames: frames in which a system with zero net force keeps constant velocity.

UnderstandInterpret and connect

In an accelerating frame, a free object may appear to accelerate even when no external interaction explains that change.

DeepenFormulation and conditions

The first law establishes the class of frames in which Newton's laws have their standard form; it is not merely the second law with zero substituted.

ExploreConnections for further study

Every frame moving at constant relative velocity with respect to an inertial frame is also inertial in Galilean mechanics.

Concept review

Common errors

Each warning includes a concrete way to review the reasoning, not only an incorrect-answer marker.

Assuming every moving object needs a forward net force.

Net force is required to change velocity; constant velocity can persist with zero net force.

Reading zero net force as the absence of individual forces.

Make the complete inventory and add vectors: nonzero forces can balance.