Newton's Laws of Motion

Newton's laws of motion are the three axioms that form the foundation of classical mechanics, first stated by Isaac Newton in his Philosophiæ Naturalis Principia Mathematica (1687). They are not derived from deeper principles within classical physics; they are the starting point. Everything else — orbits, collisions, tides, gyroscopes — follows from them.

First Law (Inertia): A body remains at rest, or in uniform motion in a straight line, unless acted upon by a force. This defines an inertial reference frame — a coordinate system in which the law holds. The law is not merely descriptive; it is a criterion for what counts as 'no force.'

Second Law (F = ma): The acceleration of a body is proportional to the net force acting upon it and inversely proportional to its mass. The vector equation F = ma is the dynamical core of Newtonian mechanics. It is not a definition of force (as some textbooks claim) but a quantitative relationship between force, inertia, and change of motion.

Third Law (Action-Reaction): For every action there is an equal and opposite reaction. Forces never occur in isolation; they come in pairs. This law underlies the conservation of momentum and is the reason rockets work in vacuum.

The laws are deceptively simple. Their application to real systems — constrained motion, rotating bodies, fluids — requires mathematical machinery (calculus, vector analysis, differential equations) that took two centuries to develop. The laws themselves are three sentences. Their consequences are infinite.