Newton's First Law of Motion

Newton's First Law of Motion: an object remains at rest, or continues to move with uniform velocity in a straight line, unless an unbalanced external force acts on it. The word "unbalanced" is doing all the work here — a body can have several forces acting on it and still obey the First Law perfectly, as long as those forces cancel out to a net force of zero.

Two halves of one idea. The law covers two situations with a single rule. If a body is at rest, it stays at rest unless a net force pushes or pulls it. If a body is already moving, it continues at the same speed, in the same straight line, unless a net force speeds it up, slows it down, or bends its path. Nothing in the law treats "rest" and "steady motion" differently — both are simply states that persist until disturbed. We can write this compactly as a condition on the net force:

where: $\vec{F}_{\text{net}}$ is the vector sum of every force acting on the body; "state of motion unchanged" means the body's velocity — both speed and direction — stays exactly as it was, whether that velocity is zero (rest) or some constant nonzero value (uniform straight-line motion).

Why it is called the Law of Inertia. Inertia is the natural reluctance of matter to change its own state of rest or motion. A body cannot start moving, stop moving, speed up, slow down, or turn by itself — some external unbalanced force is always required to produce any of these changes. The First Law is essentially a formal statement of this reluctance: it tells us what happens (nothing changes) when no net force acts, which is exactly why it is also called the Law of Inertia rather than simply "Newton's rule."

The misconception it corrects. Ordinary experience suggests that a cart needs continuous pushing to keep rolling, and that a moving object naturally "runs out" of motion and stops on its own. This was Aristotle's view for centuries. Newton's First Law says the opposite: a moving body needs zero net force to keep moving at constant velocity forever. Real objects stop because friction with the ground and air resistance are unbalanced forces acting against the motion — remove those, as on a frictionless surface, and the object would coast indefinitely.

The goal of this reasoning is to show, without needing a formula beyond the idea of balanced and unbalanced forces, exactly why a body left with zero net force cannot change its own velocity — and why that single fact accounts for both a body staying at rest and a body coasting forever in a straight line, two situations that at first look completely different.

Step 1. Recognise that changing motion always means changing velocity — starting from rest, stopping, speeding up, slowing down, or turning are all changes in speed or direction. A body has no internal mechanism to alter its own velocity; every one of these changes, in every case ever observed, traces back to some external push or pull acting on the body.

Step 2. Separate "a force acts" from "a net force acts." A book on a table has two forces on it — its weight and the table's normal force — yet it does not move, because those two forces are equal and opposite and cancel exactly. The presence of forces is not what changes motion; only an unbalanced leftover force, after all the individual forces are added as vectors, can do that.

Step 3. Apply this to a body at rest. With the forces balanced, the net force is zero, so by the reasoning in Step 1, there is nothing available to change the body's velocity from zero. It remains at rest — not because "resting is natural," but because there is genuinely no unbalanced force to move it.

Step 4. Apply the same reasoning to a moving body. On a frictionless surface, there is no horizontal force at all, and the vertical forces (weight and support) cancel just as they did for the book. The net force is again zero, so the moving body's velocity cannot change — it keeps the same speed and same direction indefinitely. The only reason moving objects around us behave differently is that friction and air resistance supply the unbalanced force that Steps 1–3 say is necessary to slow them down.

A hockey puck slides on a smooth, frictionless sheet of ice with a constant velocity of $4\ \text{m/s}$ in a straight line, and no one touches it after the initial push. Using the First Law, describe its motion after $10$ seconds, and explain what would happen differently if the puck were instead sliding across a rough, sanded patch of ice.

Step 1. Identify the forces on the puck on the frictionless stretch. Gravity pulls it down; the ice's support force pushes it up; these are equal and opposite, so they cancel. There is no horizontal friction because the ice is frictionless. The net force on the puck is zero.

Step 2. Apply the First Law. With zero net force, the puck's state of uniform motion cannot change — same speed, same straight-line direction — for as long as no unbalanced force acts on it.

Step 3. State the outcome after $10$ seconds. The puck is still moving in a straight line at $4\ \text{m/s}$; it has neither sped up, slowed down, nor changed direction. The puck's velocity after 10 s remains 4 m/s in the original direction.

Step 4 — contrast with the rough patch. On sanded ice, friction acts backward on the puck, opposing its motion. This friction is now an unbalanced horizontal force, so the net force is no longer zero, and by the same law the puck's velocity must change — it slows down and eventually stops. This is exactly why real pucks on real ice slow down: not because motion "wears off," but because friction supplies the unbalanced force the First Law requires for any change in velocity.

• "A moving object always needs a force to keep moving." The Aristotelian misconception the First Law corrects — constant velocity in a straight line needs zero net force, not a continuous push.
• Forgetting the law covers rest and uniform motion equally. Many students remember only "stays at rest" and forget it equally describes a body moving steadily forever.
• Confusing "no net force" with "no forces at all." A body can have several forces acting on it and still satisfy the First Law, as long as those forces are balanced.
• Reading everyday deceleration as the First Law "wearing off." A rolling ball stops because of friction, an unbalanced force — not because its motion has a natural expiry.

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