Newton's First Law (Inertia)

Newton's first law says that if the net external force on an object is zero, its velocity stays constant. So an object either remains at rest or keeps moving in a straight line at constant speed.

This statement applies in an inertial frame, which means a non-accelerating reference frame. The law is also called the law of inertia because inertia is the tendency of matter to resist changes in velocity.

Newton's First Law In One Line

In an inertial frame,

$$\sum \vec{F}_{\text{ext}} = 0 \Rightarrow \vec{v} = \text{constant}$$

The word "constant" matters. A constant velocity can be zero, which means rest, or it can be any steady straight-line motion.

What Inertia Means In Plain Language

People sometimes say that moving objects "want to keep moving." That is close, but incomplete. The more precise idea is that objects do not change velocity unless a net external force acts.

Velocity includes direction as well as speed. So turning counts as a change in velocity even if the speed stays the same. If the direction changes, the net external force is not zero.

Worked Example: A Puck Sliding On Smooth Ice

Suppose a hockey puck is already sliding east at $3\ \mathrm{m/s}$. After the stick loses contact, imagine the ice is smooth enough that friction is negligible for the next few seconds.

Then the net external force is approximately zero, so Newton's first law predicts that the puck keeps moving east at about $3\ \mathrm{m/s}$ in a straight line.

If the puck slows down, that tells you the net external force was not actually zero. On real ice, friction and air drag usually make the speed decrease a little, so the constant-velocity prediction is only as good as that approximation.

This is the main habit to build: first ask whether the net external force is zero. If it is, expect constant velocity. If the velocity changes in size or direction, the net external force cannot be zero.

Common Mistakes With Newton's First Law

• Thinking a force is needed to keep an object moving at constant velocity. A net force is needed to change velocity, not to maintain it.
• Treating "zero force" as the same as "zero motion." Zero net force can also mean steady motion.
• Forgetting that a turn changes velocity. Circular motion is not an example of Newton's first law because the direction keeps changing.
• Calling inertia a push or pull. Inertia is a property of matter, not an extra force.

When Newton's First Law Is Used

Newton's first law is the starting point for force analysis. Before calculating anything, you ask whether the motion suggests zero net force or nonzero net force.

It also explains why seat belts matter. When a car stops suddenly, your body tends to keep its previous velocity. The belt provides the external force that changes that motion safely.

In introductory physics, the law is also used to justify simple models. For example, horizontal projectile motion is often treated as constant-velocity motion when air resistance is ignored, because the horizontal net force is then taken to be zero.

Try A Similar Case

Try your own version with one everyday situation: a book resting on a table, a puck gliding after a hit, or a passenger lurching forward when a car brakes. Start with one question: is the net external force zero? That check usually tells you whether Newton's first law applies directly or whether you need Newton's second law next.