Newton's Three Laws of Motion: What They Actually Say

What the first law actually says

A body at rest stays at rest. A body in motion keeps moving in a straight line, at the same speed, until something acts to change that. That’s the principle of inertia, and it’s subtler than it sounds: in everyday life we’re used to thinking things “stop on their own,” because in practice friction and air resistance are almost always at work. But that friction is itself an external force: take it away, as with a puck gliding across an air hockey table, and the motion continues for much longer — the same principle that lets a football keep rolling across a well-mowed pitch, where friction is minimal (see also the Recap on the history of football’s rules).

Inertia is a body’s tendency to resist changes to its state of motion: a boulder has more of it than a basketball, meaning it resists harder when you try to speed it up or bring it to a stop. That idea leads straight to something more technical but important: the inertial reference frame, a frame in which the first law actually holds. A train moving at constant speed is (approximately) an inertial frame: a glass of water on its little table stays put relative to the train. A train braking hard is no longer one: the glass slides forward, not because some mysterious force pushes it, but because the train, the reference frame, is accelerating while the glass, by inertia, would otherwise keep going as before.

Practical example: buckling a seatbelt in a car is a direct application of the first law. In a sudden stop, the car’s cabin decelerates quickly, but by inertia, passengers’ bodies would keep moving forward at the previous speed. The seatbelt supplies the force that decelerates the body along with the car, instead of letting it carry on toward the windshield.

Even Earth, taken as the reference for everyday experiments, isn’t a perfectly inertial frame: it spins on its axis and orbits the Sun, so it accelerates slightly. That acceleration, though, is less than 3.4×10⁻² m/s², small enough to make labs on Earth “approximately inertial” for the vast majority of practical purposes, from school physics experiments to a game of football.

The second law: force, mass, and acceleration

If the first law describes what happens without a net force, the second describes what happens when there is one. An object’s acceleration is proportional to the force it receives and inversely proportional to its mass: a stronger push accelerates it more, but the same push accelerates a heavier object less. In the form taught in school, with constant mass, this is written F = m · a.

The unit of force, the newton, is defined directly from this law: one newton (1 N) is the force needed to accelerate a 1 kg object at 1 meter per second, per second. A small apple weighs about 1 N on Earth, a handy way to get a feel for just how small this unit is.

Practical example: a lawnmower pushed with a net force of 51 N and a mass of 24 kg gets an acceleration of a = F/m = 51/24 ≈ 2.1 m/s². It’s a direct application of the second law, the same one you’d use for any object, as long as you know the net force and the mass.

This brings up one of the most confused distinctions in school physics: mass and weight aren’t the same thing. Mass is an intrinsic property of an object, the amount of matter it’s made of, and it never changes, whether the object is on Earth, in orbit, or on the Moon. Weight, by contrast, is the force with which gravity pulls that mass downward: w = m · g, where g is the local gravitational acceleration. On Earth, g is about 9.80 m/s², so a 1 kg object weighs 9.80 N. On the Moon, where g is about 1.62 m/s², the same 1 kg mass weighs only 1.6 N: the matter is identical, but the force gravity exerts on it is much weaker. Everyday confusion is made worse by household scales, which display a value in “kg” but actually measure weight, calibrated to report mass under Earth’s gravity.

A finer distinction still, found in more advanced physics texts, is the one between inertial mass and gravitational mass. Inertial mass is the one that shows up in the second law, F = m · a: it measures how much an object resists being accelerated. Gravitational mass, instead, measures how much an object generates or experiences gravitational attraction. In Newtonian mechanics the two turn out to be numerically equal, a fact that lets the mass cancel out when calculating gravitational acceleration (which is why a feather and a lead weight fall at the same rate, absent air resistance), but Newton simply took this for granted without explaining it; centuries later, Einstein would elevate it to a founding principle of general relativity.

When a system’s mass isn’t constant, as with rockets burning fuel during flight, F = m · a is no longer enough: the more general form, tied to the rate of change of momentum, is needed instead.

Practical example: the Saturn V rocket, used for the Apollo missions to the Moon, had a launch mass of 2.80×10⁶ kg, about 98.9% of which was fuel. Burning 1.40×10⁴ kg of fuel per second, with exhaust gases expelled at roughly 2.40×10³ m/s, its initial acceleration was about 2.20 m/s². That’s also why large rockets are built in multiple stages: as fuel runs out, dropping the empty stages reduces the mass that still needs accelerating.

The third law: action and reaction, but on different bodies

The third law says that whenever one body exerts a force on a second body, the second exerts a force on the first that’s equal in strength and opposite in direction. It’s probably the most quoted in everyday language (“for every action there’s an equal and opposite reaction”) and also the most misunderstood, because the wording invites a specific mistake: thinking the two forces, being equal and opposite, cancel each other out.

They never do, for a simple reason: they act on two different bodies, not the same one. When a swimmer pushes off the pool wall backward with her feet, the wall pushes her forward with an equal and opposite force, and it’s that second force, acting on the swimmer’s own body, that determines her motion. If both forces acted on the same object, they really would cancel out, and nobody would ever be able to push off from a stop, which isn’t what happens every day in a pool, on a bike, or just walking.

Practical example: a regulation baseball weighs about 142 grams (5 ounces). Three forces act on it at once in flight: its weight, always pointed toward the center of the Earth; air drag, which opposes its motion and grows with the square of its speed; and lift generated by the ball’s spin (the Magnus effect), perpendicular to its path. It’s the combination of these three forces, not any single one, that shapes the curve the ball traces through the air.

The most instructive example of the third law, though, is probably rockets. A common idea pictures a rocket moving by “pushing against” the air behind it, the way a swimmer pushes against water. That’s wrong: rockets work perfectly well in the vacuum of space, where there’s nothing to push against. Their thrust comes from expelling exhaust gases at high speed: the rocket pushes the gases backward, and the gases push the rocket forward, exactly as the third law predicts. Because a rocket carries both its fuel and the oxidizer needed to burn it, it doesn’t need an atmosphere to generate thrust; if anything, it works better without one, since the exhaust gases meet less resistance expanding outward. The same principle explains why a helicopter flies by pushing air downward and receives, in reaction, an upward push.

Not exactly what Newton wrote

This Recap talks about what the three laws “actually” say because there’s a real difference, not just a stylistic one, between the version taught in school and what Isaac Newton put on paper in the 1600s. In the Philosophiae Naturalis Principia Mathematica, published in 1687, the second law isn’t stated as F = m · a, but as a proportionality between the force impressed on a body and the resulting “change of motion,” in modern terms, the rate of change of momentum. F = m · a is a later rewrite, valid when mass stays constant, and a special case (if the most common one in everyday life) of Newton’s more general law.

Early versions of the three laws date back to 1666, when Newton, barely into his twenties, was at Cambridge during the university’s closure for a plague outbreak. It took years, though, plus a push from the astronomer Edmond Halley, for those ideas to become the work we know today. In August 1684, Halley asked Newton what orbit a body would follow under a force inversely proportional to the square of the distance; discovering that Newton had already solved the problem, he convinced him to write it up in full. From a short initial treatise titled De Motu (“On Motion”), the Principia grew over roughly two and a half years of work. Historians agree the final publication came in 1687, even though an earlier version of the text had already been presented to the Royal Society the year before.

The title of the work itself is a clue to its place in the history of science. According to the Stanford Encyclopedia of Philosophy, Newton chose it in deliberate allusion to René Descartes’ Principia Philosophiae, to set his own physics, grounded in universal gravitation, against Cartesian physics, which explained planetary motion through vortices of fine matter supposedly sweeping the planets along. With Galileo Galilei, the relationship is one of continuity rather than contrast: Newton’s general laws of motion include, as special cases, Galileo’s findings on falling bodies (an object falls a distance proportional to the square of the time) and on the parabolic path of projectiles, both confirmed by experiment.

Where Newton’s laws stop

The three laws describe, with enormous precision, the world we can touch and measure directly: from lawnmowers to rockets, from baseballs to cars. But they remain laws with a defined range of application, and in two extreme situations they stop being enough.

When speeds approach that of light, the classical F = m · a relationship no longer holds, because an object’s mass no longer behaves as a fixed quantity. In a sense, this calls for returning to Newton’s original formulation: force needs to be defined more generally as the rate of change of momentum over time, an idea that relativity inherits and develops further. At the atomic and subatomic scale, meanwhile, Newton’s laws give way to quantum mechanics, which describes phenomena like interference that have no equivalent in classical physics.

None of these limits takes anything away from the three laws within their own domain: from bridge design to satellite launches, Newtonian mechanics remains the reference toolkit for calculation, so much so that it only fully matured as an organized discipline in the second half of the 1700s, once its theoretical promises had finally been worked out in full. To see how these same forces hold together bodies far larger than a rocket, the Recap on the solar system is worth a look; for a historical application of the laws of motion beyond Earth’s atmosphere, there’s the one on the Apollo 11 Moon landing.