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: the object either remains at rest or keeps moving in a straight line at constant speed. As a working relation in an inertial frame (a non-accelerating reference frame),

Here $\sum \vec{F}_{\text{ext}}$ is the net external force and $\vec{v}$ is the velocity. The law is also called the law of inertia, because inertia is the tendency of matter to resist changes in velocity. The word "constant" is doing real work: a constant velocity can be zero, which means rest, or any steady straight-line motion.

Why This Holds: Inertia In Plain Terms

People sometimes say moving objects "want to keep moving." That is close but incomplete. The precise idea is that objects do not change velocity unless a net external force acts. Velocity includes direction as well as speed, so a turn counts as a change in velocity even when the speed is unchanged. If the direction changes, the net external force is not zero. This is the intuition behind the formula: with nothing pushing the net balance off zero, there is no reason for the velocity vector to change at all.

Worked Example: A Puck Sliding On Smooth Ice

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

Then the net external force is approximately zero:

So the law predicts the puck keeps moving east at about $3\ \mathrm{m/s}$ in a straight line. If the puck instead 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.

The 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.

Check It Yourself

Pick one everyday situation: a book resting on a table, a puck gliding after a hit, or a passenger lurching forward when a car brakes. For each, start with one question: is the net external force zero? Predict constant velocity (which includes rest) when it is, and predict a change when it is not. That single check tells you whether the first law applies directly or whether you need Newton's second law next. A quick way to confirm your reasoning: if you claim zero net force but the object is turning, you have made a sign or direction error somewhere, because turning is a velocity change.

Calculation Traps To Avoid

• 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 the 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

The 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, and the belt provides the external force that changes that motion safely. In introductory physics it justifies simple models too; 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.

Frequently Asked Questions