Newton's Three Laws of Motion

Chapter 1 built the vocabulary for describing motion. This chapter answers the deeper question: what actually causes motion to change? The answer comes from one book, published in 1687, that is still the working foundation of engineering three and a third centuries later — though, as with Galileo's own falling-body story from Chapter 1, the real history behind it is less tidy than the popular version.

The Three Laws: A Real, Layered History

Isaac Newton did not invent the idea of inertia from nothing. His Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), published in 1687, is correctly credited with the first fully rigorous, mathematical statement of the three laws — but each law has real intellectual ancestors that Newton himself built on and synthesized.

Galileo, in the same 1638 book Two New Sciences that Chapter 1 covered for falling bodies, described what historians now call "circular inertia": a body moving on a level surface continues at constant speed unless disturbed. Galileo's own version was subtly different from Newton's later law — because Galileo was working within an Earth-centered picture of "level," his inertia applied to motion that curved gently along the Earth's own surface, not motion in a truly straight line through empty space.

René Descartes, in his 1644 Principles of Philosophy, contributed from a different direction: a broader physical framework in which matter and space were treated as geometrically identified, and motion was conserved as a fundamental quantity (his own "quantitas motus," a real forerunner of the momentum concept this chapter's own second law depends on). Newton's real achievement in 1687 was not inventing these ideas in isolation, but refining, correcting, and mathematically unifying them into three laws precise enough to predict planetary orbits, cannonball trajectories, and tides with genuine numerical accuracy.

The First Law: Inertia

The First Law says that an object's velocity — both its speed and its direction — does not change on its own. A book resting on a table stays at rest; a hockey puck sliding on frictionless ice keeps sliding in a straight line forever. Nothing about motion itself requires a continuous push to sustain it — a genuinely counterintuitive idea to anyone reasoning from everyday experience with friction, which is precisely why it took until the 17th century to state clearly.

Inertia is the name for this resistance to a change in velocity, and mass is its real, quantitative measure: a bowling ball resists a change in its motion far more than a table-tennis ball does, for exactly the same applied push.

The Second Law: Force and the Rate of Change of Motion

The Second Law is the one most people can already recite — F = ma — but Newton's own 1687 statement was not phrased that way at all. Newton wrote: "The change of motion of an object is proportional to the force impressed; and is made in the direction of the straight line in which the force is impressed." "Motion," to Newton, meant what we now call momentum — mass multiplied by velocity (p = mv) — not velocity alone.

In modern calculus notation, Newton's real law reads F = dp/dt: force equals the rate of change of momentum. When mass stays constant (the overwhelming majority of everyday mechanics problems), this reduces cleanly to the familiar form:

Worked Example: A Shopping Trolley

A loaded shopping trolley has a mass of 25 kg. A shopper pushes it with a steady force of 15 N. What is its acceleration?

The trolley speeds up by 0.6 m/s every second the push continues — matching Chapter 1's own SUVAT equations exactly, since a constant force produces a constant acceleration, which is exactly the kind of motion SUVAT describes.

Mass Is Not Weight

Mass (measured in kilograms) is a body's real resistance to acceleration — it does not change if you take the same object to the Moon. Weight is the real gravitational force acting on that mass (measured in newtons, W = mg), and it does change with location, since the Moon's own gravitational acceleration is roughly one-sixth of Earth's. A 25 kg trolley has the same 25 kg mass on the Moon — and the same real resistance to being pushed — even though it would weigh far less there.

The Third Law: Action and Reaction

Newton's own real wording: "To every action there is always opposed an equal reaction; or, the mutual actions of two bodies upon each other are always equal, and directed to contrary parts." Forces never occur alone — they come in genuinely equal, opposite pairs acting on two different objects.

A common misreading treats the two forces as somehow cancelling out, but they act on different bodies and never cancel within a single object's own motion. When you walk, your foot pushes backward against the ground; the ground pushes forward against your foot with equal force — and it is that second force, acting on you, that actually propels you forward. A rocket's engine pushes exhaust gas backward at enormous speed; the exhaust gas pushes the rocket forward with equal force — the real mechanism behind rocket propulsion, and one that works identically in the vacuum of space, since it depends on the rocket's own expelled mass, not on pushing against surrounding air.

The Three Laws, Compared

Hands-On Exercises

Next chapter: Work, Energy & Power — where a force acting over a distance becomes work, and the real principle of conservation of energy enters the picture.