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Newton's laws of motion

Three foundational principles by Isaac Newton that describe how forces affect motion in classical mechanics and underpin much of engineering and physics.

Author: Leandro Alegsa Creation date: November 13, 2022 Last updated: May 16, 2026

simple.wikipedia.org · Public domain

Isaac Newton formulated three fundamental principles in the 17th century that form the foundation of classical mechanics. Collectively called Newton's laws of motion, they describe the relationship between forces acting on bodies and the motion that results. These principles provide a simple framework for analyzing everyday phenomena from falling apples to planets in orbit, and they remain central to engineering and basic physics instruction.

The three laws

First law (inertia): An object at rest stays at rest and an object in motion continues in uniform motion in a straight line unless acted on by a net external force. This law expresses the concept of inertia — resistance to changes in motion — and defines an inertial reference frame in which the law holds.
Second law (relation of force, mass, and acceleration): The acceleration of an object is proportional to the net force acting on it and inversely proportional to its mass. In formulaic form this is commonly written as F = ma, where F is the net force, m the mass, and a the acceleration. The second law provides a quantitative rule to predict how motion changes when forces are applied.
Third law (action and reaction): For every action there is an equal and opposite reaction. When one body exerts a force on a second body, the second exerts a force of the same magnitude and opposite direction on the first. This principle explains propulsion, collisions, and many equilibrium situations.

Historical context and development

Newton introduced these laws in his work on motion and universal gravitation, synthesizing earlier ideas about movement and force. The laws were articulated as part of a larger mathematical framework that also described gravitation and planetary motion. Over subsequent centuries they were tested, refined in application, and incorporated into the broader subject of dynamics. Experimental observations and practical engineering validated their usefulness for a wide range of scales and speeds.

Uses, examples, and importance

Newton's laws are used to analyze mechanical systems from simple machines to complex structures. Examples include calculating the acceleration of vehicles, predicting projectile trajectories, designing stable buildings, and understanding orbital motion. Textbooks and laboratories commonly demonstrate the laws with experiments and measurements; experimental agreement with predictions reinforced their authority in classical physics (experimental confirmations).

Limits and later developments

While extremely accurate for everyday speeds and sizes, Newton's laws are an approximation. They are superseded by Einstein's theories of relativity at velocities close to the speed of light and by quantum mechanics at atomic scales. Nevertheless, within their domain they remain highly effective and are often the simplest adequate model for engineering and most scientific work in the macroscopic world (classical mechanics).

Common distinctions and notable facts

The first law establishes the reference frame concept that distinguishes inertial frames from accelerating frames; analyzing motion correctly often requires attention to the observer's frame (study of motion).
F = ma (second law) gives a practical method to compute forces or accelerations but care is needed in systems where mass changes or where forces depend on velocity.
The third law is central to understanding interactions: rockets move forward because exhaust gases are pushed backward, and contact forces between objects always come in pairs.

Together, Newton's laws form a concise, powerful set of principles that explain a vast range of physical behavior and remain foundational to science education and many applied fields.

Newton's first and second laws, in Latin, from the original 1687 edition of Principia Mathematica.

Newton's first law

Newton's first law is also called lex prima, principle of inertia, law of inertia or inertial law. The principle of inertia makes statements about the motion of physical bodies in inertial systems. There are different versions:

"A body remains in a state of rest or uniform rectilinear motion unless it is forced to change its state by acting forces."

Original Latin text:

Corpus omne perseverare in statu suo quiescendi vel movendi uniformiter in directum, nisi quatenus illud a viribus impressis cogitur statum suum mutare.

The velocity ${\vec {v}}$ is therefore constant in magnitude and direction. A change in the state of motion can only be achieved by exerting a force from outside, for example the gravitational force or the frictional force.

Other versions read:

If no force acts on a body, its velocity is constant in time.

If no force acts on a mass point, its momentum is constant. The momentum is the product of mass and velocity.

In these forms, the theorem only applies if no force is acting at all. The converse, that no force acts when he is moving at constant speed, does not follow from this. In this case, several forces can also act on him, cancelling each other out in their effect. In this case, no resulting force acts.

For a point of mass, Newton's first law corresponds to the equilibrium conditions. For extended bodies, the angular momentum equilibrium must also be checked.

Galileo Galilei was the first to recognize the principle of inertia at the beginning of the 17th century and also already formulated that force-free motion continues in a straight line for any distance. He used this for the first correct treatment of the movements of bodies on earth in free fall, in inclined throw and on the inclined plane. The first unambiguous formulation as a general principle of force-free motion was given by René Descartes in 1644, but it was Newton who first applied the principle of inertia to the motions of extraterrestrial bodies. This is also his special achievement: in the works of antiquity, which were still considered correct until the late Middle Ages, it was believed that the motions on Earth and those in the heavens obeyed different laws. Newton recognized them as two special cases of a general law. Moreover, Newton thus declared rectilinear, unaccelerated motion to be the normal case. Only if the motion of a body deviates from this, must this be explained by the effect of forces. Shortly before Newton, it was assumed that circular motion was the normal case.

The above versions are only valid if the motion is described in an inertial frame. Newton's first law is then merely a special case of the second. In modern works on theoretical mechanics, the reference frame is usually defined first and Newton's first axiom is then introduced in one of the following versions or similar versions.

There are reference systems in which force-free motion occurs at a constant speed. These are inertial systems.

There are coordinate systems in which every force-free mass point moves or rests uniformly in a straight line. These particularly important coordinate systems are called inertial systems.

Then it is determined which properties must apply to inertial systems. (In particular, they must not rotate or be accelerated.) Newton's first axiom is thus used as a definition for the concept of an inertial system.

See also: Importance of inertia for important principles of mechanics

Newton's Third Law

→ Main article: Actio and Reactio

Newton's third law, also called the lex tertia, interaction principle, counteraction principle, or reaction principle, states:

"Forces always occur in pairs. If a body A exerts a force on another body B (actio), an equal but opposite force is exerted by body B on body A (reactio). “

Original Latin text:

"Actioni contrariam semper et aequalem esse reactionem: sive corporum duorum actiones in se mutuo semper esse aequales et in partes contrarias dirigi. "

${\vec {F}}_{{A\to B}}=-{\vec {F}}_{{B\to A}}$

The principle of interaction is also called the principle of actio and reactio or in short "actio equals reactio" (lat. actio est reactio). Newton's third law presupposes a direct action at a distance. Therefore, it has no general validity in special relativity (and thus electrodynamics) and general relativity - here, rather, the conservation of momentum of the entire system (particles plus radiation) applies. The interaction principle can also be formulated in such a way that in a closed system the sum of the forces is equal to zero, which is equivalent to the conservation of momentum.

Questions and Answers

Q: Who is known as the father of dynamics?

A: Isaac Newton is known as the father of dynamics.

Q: What did Isaac Newton develop?

A: Isaac Newton developed three laws that serve as the foundation of classical mechanics.

Q: Why are Isaac Newton's laws believed to be true?

A: Isaac Newton's laws are believed to be true because the results of experiments by scientists agree with his laws.

Q: What is dynamics?

A: Dynamics is the study of motion.

Q: How many laws did Isaac Newton develop?

A: Isaac Newton developed three laws.

Q: What is the significance of Isaac Newton's laws of motion?

A: Isaac Newton's laws of motion are significant because they are the foundation of classical mechanics.

Q: What was Isaac Newton's contribution to the field of physics?

A: Isaac Newton's contribution to the field of physics was the development of three laws that serve as the foundation of classical mechanics.