# Physics of Newtonian Dynamics

 Newtonian Dynamics
In law variety a pair of, the acceleration lasts solely whereas the applied force lasts. The applied force needn't, however, be constant in time — the law is true in the slightest degree times throughout the motion. Law variety three applies to “contact” interactions. If the bodies area unit separated, and also the interaction takes a finite time to propagate between the bodies, the law should be changed to incorporate the properties of the “field “ between the bodies.

Although our discussion of the geometry of motion has led to major advances in our understanding of measurements of space and time in different inertial systems, we have yet to come to the crux of the matter, namely — a discussion of the effects of forces on the motion of two or more interacting particles. This key branch of Physics is called Dynamics. It was founded by Galileo and Newton and perfected by their followers, most notably Lagrange and Hamilton. We shall see that the Newtonian concepts of mass, momentum and kinetic energy require fundamental revisions in the light of the Einstein’s Special Theory of Relativity. The revised concepts come about as a result of Einstein's recognition of the  crucial rôle of the Principle of Relativity in unifying the dynamics of all mechanical and optical phenomena. In spite of the conceptual difficulties inherent in the classical concepts, (difficulties that will be discussed later), the subject of Newtonian dynamics represents one of the great triumphs of Natural Philosophy. The successes of the classical theory range from accurate descriptions of the dynamics of everyday objects to a detailed understanding of the motions of galaxies.

The law of inertia
Galileo (1544-1642) was the first to develop a quantitative approach to the study of motion. He addressed the question — what property of motion is related to force? Is it the position of the moving object? Is it the velocity of the moving object? Is it the rate of change of its velocity? ...The answer to the question can be obtained only from observations; this is a basic feature of Physics that sets it apart from Philosophy proper.

Galileo observed that force influences the changes in velocity (accelerations) of an object and that, in the absence of external forces (e.g: friction), no force is needed to keep an object in motion that is travelling in a straight line with constant speed. This observationally based law is called the Law of Inertia. It is, perhaps, difficult for us to appreciate the impact of Galileo's new ideas concerning motion. The fact that an object resting on a horizontal surface remains at rest unless something we call force is applied to change its state of rest was, of course, well-known before Galileo's time. However, the fact that the object continues to move after the force ceases to be applied caused considerable conceptual difficulties for the early Philosophers (see Feynman The Character of Physical Law). The observation that, in practice, an object comes to rest due to frictional forces and air resistance was recognized by Galileo to be a side effect, and not germane to the fundamental question of motion. Aristotle, for example, believed that the true or natural state of motion is one of rest. It is instructive to consider Aristotle's conjecture from the viewpoint of the Principle of Relativity —- is a natural state of rest consistent with this general Principle? According to the general Principle of Relativity, the laws of motion have the same form in all frames of reference that move with constant speed in straight lines with respect to each other. An observer in a reference frame moving with constant speed in a straight line with respect to the reference frame in which the object is at rest would conclude that the natural state or motion of the object is one of constant speed in a straight line, and not one of rest. All inertial observers, in an infinite observations; this is a basic feature of Physics that sets it apart from Philosophy proper.

Galileo observed that force influences the changes in velocity (accelerations) of an object and that, in the absence of external forces (e.g: friction), no force is needed to keep an object in motion that is travelling in a straight line with constant speed. This observationally based law is called the Law of Inertia. It is, perhaps, difficult for us to appreciate the impact of Galileo's new ideas concerning motion. The fact that an object resting on a horizontal surface remains at rest unless something we call force is applied to change its state of rest was, of course, well-known before Galileo's time. However, the fact that the object continues to move after the force ceases to be applied caused considerable conceptual difficulties for the early Philosophers (see Feynman The Character of Physical Law). The observation that, in practice, an object comes to rest due to frictional forces and air resistance was recognized by Galileo to be a side effect, and not germane to the fundamental question of motion. Aristotle, for example, believed that the true or natural state of motion is one of rest. It is instructive to consider Aristotle's conjecture from the viewpoint of the Principle of Relativity —- is a natural state of rest consistent with this general Principle? According to the general Principle of Relativity, the laws of motion have the same form in all frames of reference that move with constant speed in straight lines with respect to each other. An observer in a reference frame moving with constant speed in a straight line with respect to the reference frame in which the object is at rest would conclude that the natural state or motion of the object is one of constant speed in a straight line, and not one of rest. All inertial observers, in an infinite number of frames of reference, would come to the same conclusion. We see, therefore, that Aristotle's conjecture is not consistent with this fundamental Principle.

Newton’s laws of motion
During his early twenties, Newton postulated three Laws of Motion that form the basis of Classical Dynamics. He used them to solve a wide variety of problems including the dynamics of the planets. The Laws of Motion, first published in the Principia in 1687, play a fundamental rôle in Newton’s Theory of Gravitation; they are:
1. In the absence of an applied force, an object will remain at rest or in its present state of constant speed in a straight line (Galileo's Law of Inertia)
2. In the presence of an applied force, an object will be accelerated in the direction of the applied force and the product of its mass multiplied by its acceleration is equal to the force. And,
3. If a body A exerts a force of magnitude$\left | F_{AB} \right |$ on a body B, then B exerts a force of equal magnitude $\left | F_{BA} \right |$ on A.. The forces act in opposite directions so that $\mathrm{F}_{AB}=\mathrm{F}_{BA}$  .

In law number 2, the acceleration lasts only while the applied force lasts. The applied force need not, however, be constant in time — the law is true at all times during the motion. Law number 3 applies to “contact” interactions. If the bodies are separated, and the interaction takes a finite time to propagate between the bodies, the law must be modified to include the properties of the “field “ between the bodies.

Reference:

FRANK  W. K. FIRK
Professor Emeritus of Physics
Yale University

Physics of Newtonian Dynamics