How Newton's Laws Became Laws Of Nature

Isaac Newton's three laws of motion were first published in 1687 in his work 'Philosophiæ Naturalis Principia Mathematica' (Mathematical Principles of Natural Philosophy). These laws describe the motion of massive bodies and how they interact. They form the basis for classical mechanics, which is the study of massive objects that are larger than the very small scales addressed by quantum mechanics and that are moving slower than the very high speeds addressed by relativistic mechanics. Newton's laws were considered revolutionary at the time and have been verified by countless experiments over the past three centuries.

The laws were first published in 1687 in Newton's work 'Philosophiæ Naturalis Principia Mathematica'

Newton's laws were first published in 1687 in his work *Philosophiæ Naturalis Principia Mathematica* (known in English as *Mathematical Principles of Natural Philosophy*) . The laws form the basis for classical mechanics.

Newton's three laws of motion describe the motion of massive bodies and how they interact. They provide the relationship between the forces acting on a body and the motion of the body. Newton used them to explain many results concerning the motion of physical objects. In the third volume of the text, he showed that the laws of motion, combined with his law of universal gravitation, explained Kepler's laws of planetary motion.

Newton's first law states that an object at rest will remain at rest, and a body in motion will remain in motion unless it is acted upon by an external force. This is also called the law of inertia.

Newton's second law states that the force acting on an object is equal to the mass of that object multiplied by its acceleration. This is written in mathematical form as F = ma, where F is force, m is mass, and a is acceleration. The bold letters indicate that force and acceleration are vector quantities, meaning they have both magnitude and direction.

Newton's third law states that for every action, there is an equal and opposite reaction. Forces always occur in pairs, so when one body pushes against another, the second body pushes back just as hard.

Newton's laws have been verified by countless experiments over the past three centuries and are still widely used today. However, they break down when applied to extremely high speeds or very small objects. At extremely high speeds, Albert Einstein's Special Theory of Relativity comes into play, while quantum mechanics explains the behaviour of very small objects.

The laws form the basis for classical mechanics

Newton's laws of motion form the basis of classical mechanics. Classical mechanics is the study of massive objects that are larger than the very small scales addressed by quantum mechanics and that are moving slower than the very high speeds addressed by relativistic mechanics.

Newton's three laws of motion describe the motion of massive bodies and how they interact. They are:

First Law of Motion

> A body at rest will remain at rest, and a body in motion will remain in motion unless it is acted upon by an external force.

This means that things cannot start, stop, or change direction all by themselves. It takes some force acting on them from the outside to cause such a change. This property of massive bodies to resist changes in their state of motion is sometimes called inertia.

Second Law of Motion

> The force acting on an object is equal to the mass of that object times its acceleration.

This is written in mathematical form as F = ma, where F is force, m is mass, and a is acceleration. The bold letters indicate that force and acceleration are vector quantities, which means they have both magnitude and direction.

Third Law of Motion

> For every action, there is an equal and opposite reaction.

This law describes what happens to a body when it exerts a force on another body. Forces always occur in pairs, so when one body pushes against another, the second body pushes back just as hard.

Newton's laws were first published in his work *Philosophiæ Naturalis Principia Mathematica* in 1687. They were considered revolutionary at the time and have been verified by countless experiments over the past three centuries. They are still widely used today.

The laws describe the motion of massive bodies and how they interact

Newton's three laws of motion describe the motion of massive bodies and how they interact. The laws were first stated by Isaac Newton in his 1687 work, 'Philosophiæ Naturalis Principia Mathematica' (Mathematical Principles of Natural Philosophy). In this work, Newton formalised the description of how massive bodies move under the influence of external forces.

Newton's three laws of motion are:

• A body at rest will remain at rest, and a body in motion will remain in motion unless it is acted upon by an external force.
• The force acting on an object is equal to the mass of that object times its acceleration. This is written in mathematical form as F = ma.
• For every action, there is an equal and opposite reaction.

Newton simplified his treatment of massive bodies by considering them to be mathematical points with no size or rotation. This allowed him to ignore factors such as friction, air resistance, temperature, and material properties. Consequently, Newton's three laws cannot be used to describe precisely the behaviour of large rigid or deformable objects. However, in many cases, they provide suitably accurate approximations.

Newton's laws pertain to the motion of massive bodies in an inertial reference frame, sometimes called a Newtonian reference frame. An inertial reference frame can be described as a 3-dimensional coordinate system that is either stationary or in uniform linear motion. Newton found that motion within such an inertial reference frame could be described by his three simple laws.

The laws are valid only for motions relative to a reference frame

Newton's laws of motion describe the motion of massive bodies and how they interact. They are valid only in inertial frames of reference, also known as Newtonian reference frames. An inertial reference frame is a 3-dimensional coordinate system that is either stationary or moving at a constant velocity, i.e. it is not accelerating or rotating.

Newton's laws of motion are not valid in non-inertial frames of reference, where the observer is accelerating or rotating with respect to an inertial frame.

Newton's first law of motion states that a body at rest will remain at rest, and a body in motion will remain in motion unless it is acted upon by an external force. This means that objects cannot start, stop, or change direction by themselves, and require an external force to cause such a change.

Newton's second law of motion describes what happens to a massive body when it is acted upon by an external force. It states that the force acting on an object is equal to the mass of that object multiplied by its acceleration, written as F = ma, where F is force, m is mass, and a is acceleration.

Newton's third law of motion states that for every action, there is an equal and opposite reaction. This means that forces always occur in pairs, so when one body exerts a force on another, the second body exerts an equal force in the opposite direction.

Newton's laws were first stated in his "Philosophiæ Naturalis Principia Mathematica" (Mathematical Principles of Natural Philosophy), published in 1687. They have been verified by countless experiments over the past three centuries and are still widely used today. They form the foundation of classical mechanics, which studies massive objects larger than the scales addressed by quantum mechanics and slower than the speeds addressed by relativistic mechanics.

The laws are just as exact for quantum operators as they are for classical objects

Newton's laws of motion were first stated by Isaac Newton in his Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), originally published in 1687. They are three physical laws that describe the relationship between the motion of an object and the forces acting on it.

Newton's laws are just as exact for quantum operators as they are for classical objects. While Newton's laws are often stated in terms of point or particle masses, this is a reasonable approximation for real bodies when the motion of internal parts can be neglected, and when the separation between bodies is much larger than the size of each.

Newton's laws can be applied to fluids by considering a fluid as composed of infinitesimal pieces, each exerting forces upon neighbouring pieces. The Euler momentum equation is an expression of Newton's second law adapted to fluid dynamics.

The Ehrenfest theorem provides a connection between quantum expectation values and Newton's second law, a connection that is necessarily inexact, as quantum physics is fundamentally different from classical physics. In quantum physics, position and momentum are represented by mathematical entities known as Hermitian operators, and the Born rule is used to calculate the expectation values of a position measurement or a momentum measurement.

Classical mechanics (point particle) can follow via Ehrenfest's Theorem:

> \vec{p}=m\vec{v}

>

> \vec{F}=-\nabla V

Holds for a system with a (quantum mechanical) Hamiltonian

> H=\frac{p^2}{2m}+V(\vec{r},t)

Via expectation values.

In summary, Newton's laws of motion are just as exact for quantum operators as they are for classical objects, with some adaptations and considerations for the unique characteristics of quantum physics.

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