CM [008] Newton's Principia

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PRINCIPIACM [008] Isaac Newton’s


Sir Isaac Newton

Sir Isaac Newton (1642 – 1727) was an English physicist and mathematician (described in his own day as a "natural philosopher") who is widely recognised as one of the most influential scientists of all time and as a key figure in the scientific revolution. His discovery of the law of gravity and the laws in mechanics laid the foundations for classical mechanics. He also made seminal contributions to optics, and he shares credit with Gottfried Leibniz for the development of calculus. Wikipedia.


Principia Mathematica

The most important document in the field of physics was published in 1686 by Sir Isaac Newton through the Royal Society in his book entitled:

“Philosophiae NaturalisPrincipia Mathematica”

Which in modern day English is:

“The Mathematical Principles of Natural Science”.

Since then the kinetic behavior of a particle is completely and satisfactorily describable by his three basic theorems.

Title page of the first edition of the Principia.


On the Shoulders of Giants

The Principia has long been recognized as one of the intellectual landmarks in the history of physics. It is the first book to show clearly the close relationship between mathematics and formal logic . . . . No other book has such an influence on the subsequent history of mathematical philosophy.

A. N. Whitehead and Bertrand Russell: Principia Mathematica. Cambridge University Press. 1910.

Newton was rather modest with his own achievements. In his letter to Robert Hooke in February 1676, he wrote:

If I have seen further it is by standing on the shoulders of giants.


Epitaph

The English poet Alexander Pope wrote this famous epitaph:

Nature and nature’s law hid in night;

God said “Let Newton be” and all was light.

Figure drawing by William Blake (1757-1827). Depicting Newton as God the geometer. Originally meant to degrade Newton as a devilish draftsman.


Newton’s Three Laws of motion

In forms slightly different from the original versions, Newton’s laws of motion can be stated as follows:

Law No. ❶ : A particle in rest will remain forever at rest, and a particle in uniform rectilinear motion will continue to move on forever at constant speed in the same direction. It will change its state of motion only and only when it is compelled to do so by forces impressed on it.

Law No. ❷ :When a particle is acted on by an external force, it accelerates. The acceleration is proportional to the magnitude of the applied force 𝑭𝑭 and is in the same direction as the applied force. If the particle has a mass of 𝑚𝑚 and the applied force is represented by the vector 𝐹𝐹, then: 𝑭𝑭 = 𝑚𝑚𝒂𝒂.

Law No. ❸: Whenever one body exerts a force F onto a second body, the second body exerts the force −F on the first body. 𝑭𝑭 and −F are equal in magnitude and opposite in sense.


Foundation of Classical Mechanics

This is the first time in history that the kinetic behavior of a particle is completely and satisfactorily describable by the three theorems. Since Newton’s time these theorems of force and motion had become the very foundation of classical mechanics and accredited the status of laws.


Complete Foundation

Later on in the nineteenth century, classical mechanics was further enhanced by Albert Einstein’s special relativity and general relativity. For motion of objects with a high velocity approaching the speed of light, relativity consideration is employed. Besides a small doubt about Einstein’s theory, classical mechanics is said to be complete.


IMPETUS

IMPETUS+ Sustaine

d Motion

INERTIA

Unexpected Guest

We shall deal with this gentleman in a

later section on Relative Motion.

HIG

H SPEED


New View of the Universe

We now have established that in nature, there are different properties pertaining to motion: velocity, force, impetus and inertia.

By setting up the Laws of Mechanics, Newton established the relationship between the various elements. He showed that the same physical laws are universal and can be applied to all matter, whether living or nonliving, on earth or in space, thus revolutionizing our view of the universe.


Newton’s ‘Three Laws’

Strictly speaking, the three laws of Newton’s are actually not laws analogous to the man-made law in our common sense. They are only generalized descriptions of certain phenomena of motion. Descriptions such as the motional behaviours of objects in the first law, the relation of force and acceleration in the second law, and the action-reaction relation in the third law. That is why we draw them as columns, not truly foundations. However they are so general, so amicably applicable in practice that people just accepted them as laws – and it is convenient to do so.


Need to Re-examine the Laws

On the surface, they seem to have settled the millennia old problem of motion. But at a closer look, they are not quite what them seem to be appropriate for our discussion. Although they have created a concrete body to embrace almost all problems about motion, they have not provided an answer to the basic question – “what is impetus or momentum?”. So we have to subject the laws to a closer examination.


NEWTON’S FIRST LAW OF MOTIONTo be continued on : CM [009]

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