Newton's laws of motion

In 1687 Isaac Newton's work Philosophiae Naturalis Principia Mathematica (Latin; 'Mathematical Principles of Natural Philosophy') was published, in which Newton formulates three principles (laws) of motion known as Newton's axioms, fundamental laws of motion, Newtonian principles, or Newtonian laws. They are referred to in Newton's work as Lex prima, Lex secunda and Lex tertia ('First/Second/Third Law'), collectively as Axiomata, sive leges motus ('Axioms or Laws of Motion').

These laws form the foundation of classical mechanics. Although they do not apply without restriction within the framework of modern physical theories such as quantum mechanics and relativity, with their help reliable predictions are possible within a broad range of validity.

Most often the following three laws are mentioned, which in a highly simplified form are as follows:

1. A force-free body remains at rest or moves in a straight line at a constant speed.
2. Force equals mass times acceleration. ( )
3. Force equals opposing force: A force from body A on body B is always accompanied by an equal but opposing force from body B on body A.

Newton already assumed that two forces can be combined into one resulting force with a parallelogram of forces. The axiom of the parallelogram of forces is also called Newton's fourth law. In modern literature, however, the superposition principle is usually called Newton's fourth law.

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 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.

Newton's Third Law

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. "

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.