Definition
Newton's Laws of Motion
Newton’s three laws of motion describe the relationship between a force acting on a body and the body’s motion. They form the foundation of classical mechanics.
Laws
First Law
The first law defines the natural motion of a body: constant velocity in the absence of net external influence. It breaks with the Aristotelian view that a force is required to sustain motion. A body does not need a push to keep moving; it needs a push to change its motion.
This property is called inertia, and mass is its quantitative measure. The first law also singles out inertial frames — frames in which the law holds — as the privileged reference frames of mechanics.
Second Law
The second law quantifies how motion changes under force. It can be stated in the more general momentum form:
When mass is constant, this reduces to . The law is a vector equation: a force in one direction produces acceleration in that same direction, independently of motion in orthogonal directions.
The second law is the engine of classical mechanics. Combined with a force law (gravitational, spring, electrostatic), it yields a differential equation whose solution is the trajectory of the body.
The third law states that forces come in pairs. If you push on a wall, the wall pushes back with equal strength. This is not a statement about balance — the forces act on different bodies and therefore do not cancel in the equation of motion for either body alone.
The third law underpins conservation of momentum. In an isolated system of particles, all internal forces cancel pairwise, so total momentum is conserved.
Limits
Newton’s laws are accurate for macroscopic objects at speeds small compared to the speed of light. They break down in two regimes:
- At speeds approaching , they are superseded by special relativity.
- At atomic scales, they are superseded by quantum mechanics.
Within their domain, they remain exact for all practical purposes.