Part 2. Cartes to Newton

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FRICTION
The Discovery of

The Discovery of Friction
One important breakthrough in the study
of motion is the discovery of friction in
the seventeenth century. Friction is a
resistance force between a moving object
and the surface it moves on or the
medium it moves in. It tends to stop
motion.
The basic nature of friction was first
made aware by Leonardo Da Vinci (1452-
1519) 200 years before Newton even
defined what force is. However Leonardo
did not published his findings and the
credit of discovering friction was awarded
to the architect Guillaume Amontons
(1663-1705).
Oops!

The Unseen Genie
Friction is like an unseen genie, when you rub against a surface, it comes up and
opposes your action. It suffices here to say that the magnitude of the force depends
directly on the weight of the object and the nature of the surface. For example, on a
rough surface, it will be hard to slide on; but on ice, one can glide effortlessly. Readers
who are interested may look up the internet or read from common text books.

Different Game for Aristotle
Had Aristotle been aware of friction in his time, he would not have made so many wrong
concepts about motion, because if there were no friction in the world, anything that
starts moving would never stop. No more or further force is necessary.
Oh what a different game
I could have played!
No friction

RENE DESCARTES
The Laws of

René Descartes
René Descartes (1596–1650) was a
French philosopher and mathematician
who developed a theory known as the
mechanical philosophy. This philosophy
was highly influential until superseded by
Newton's methodology.
Carte’s achievement has be so well
received in his time that he has been
dubbed the father of modern philosophy,
and much subsequent Western
philosophy is a response to his
writings,[which are studied closely even
to this day. In particular, his Meditations
on First Philosophy continues to be a
standard text at most university
philosophy departments. Wikipedia

Definition of Motion
In the study of mechanics, Descartes
provided the first distinctly modern
formulation of laws of nature and a
conservation principle of motion.
He accepted the existence of inertial
motion (uniform or non-accelerating
motion) or bodily rest as natural bodily
states.
He regarded motion as “the action by
which some body is transferred from
one place to another”.

Size and Velocity
The quantity of motion of a body is the size of the body times its speed. This is not to be
identified with momentum (mass x velocity), because for Descartes, size and mass are
not distinct concepts; at the same time, for Descartes, speed (scalar) and velocity
(vector) are not distinct concepts.

Conservation of Motion
Descartes also envisioned the conservation of
quantity of motion as one of the fundamental
governing principles of the entire cosmos. When
God created the universe, he reasoned, a certain
finite amount of motion (quantity of motion) was
conferred to its material occupants; a quantity,
moreover, that God continuously preserves at each
succeeding moment. Part 2, Article 36.
Due to the immutability and constancy of God, the
total quantity of motion of bodies in the universe is
conserved.

Conservation of Transference
It is obvious that when God first
created the world, He not only moved
its parts in various ways, but also
simultaneously caused some of the
parts to push others and to transfer
their motion to these others. So in
now maintaining the world by the
same action and with the same laws
with which He created it, He
conserves motion; not always
contained in the same parts of
matter, but transferred from some
parts to others depending on the
ways in which they come in contact.
As to the cause of motion,
Descartes believed that God
is the primary cause, the rest
are secondary causes.
He said: Part II, Article 62.

Summary of Descartes’s Law of Motion
According to Descartes, motion is governed by the following laws:
1. Each and every thing, as far as it can, always continues in its same state – in motion
or at rest.
2. This natural tendency to preserve the present state can be affected by “external
causes”.
The second law holds that “all movement is, of itself, along straight lines” (Pr II 39) It
also deals with circular motion and is not in our discussion here.
This law is as close to Newtons laws as any pre-Newtonian philosopher can get. The
renowned historian of science Clifford Truesdell (1919-2000) had observed, “[Descartes'
physics] is the beginning of theory in the modern sense”

Nature of Impetus
As to the nature of motion and
the transferred substance,
Descartes declared that motion
and rest are primitive states of
material bodies. It does not
need of further explanation. So
from Descartes, we still do not
get any clue as to what impetus
or momentum is.
?

GALILEO GALILEE
The Resourceful

Galileo Galilei
Galileo Galilei (1564-1642) was an Italian
physicist, mathematician, engineer,
astronomer, and philosopher who played a
major role in the scientific revolution during
the Renaissance.
His achievements include improvements to
the telescope so much so that data could be
collected to support Copernicanism. Galileo
has been variously called the “father of
modern observational astronomy”, the "father
of modern physics”, the “father of science”,
and “the father of modern science”. When
Newton said that he could see further because
he was on the shoulder of giants.” Galileo is
no doubt the giant he referred to.

Inertia
One of Galileo’s important contributions to the idea of motion is the discovery of
inertia. The word ‘inertia’ comes from the Latin word, iners, which means idle,
sluggish. It describes the quality of an object to resist changes to its state of motion. If
you want to move an object, you feel its resistance and you need an effort to change it.
Inertia is the tendency of
matter to resist changes in its
velocity. Inertia look slightly
different from impetus. Inertia
is an intrinsic property of
matter. It is that property of
matter which opposes changes
in velocity.
Inertia Force

Experiment to Prove
Inertia
The proof of this idea was
that if a ball rolled down
one ramp, its inertia
would cause it to roll up
an opposite ramp of equal
height. If the ramps are
placed close to each
other, the motion will go
on for some time before
being stopped by the
effects of friction.

Conservation of Inertia
If we lower the slope of the second ramp, the ball will actually travel farther up the ramp,
but to the same height. Using this logic, as the ramp approaches a level surface, the ball
will roll forever.
The theory of inertia says that an object’s inertia has the
tendency to maintain its state of motion. The more inertia
an object has, the harder it is to change its state of motion.

Galilean Law of Inertia
Inertia is also something innate with a moving object. Galileo's Principle of Inertia
stated: “A body moving on a level surface will continue in the same direction at constant
speed unless disturbed.”
This principle was later incorporated into Newton's laws of motion (first law).

The Law of Inertia
In popular culture we often see this Law written as:
An object at rest will tend to remain at rest unless acted upon by an outside force. An
object in a constant state of motion will tend to remain in that state of motion unless
acted upon by an outside force.

The Kinetic Piece
Inertia
Thus Galileo succeeded in adding another
piece of our motion puzzle.
VelocityForce Impetus

THREE LAWS OF MOTION
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 Naturalis Principia
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 Guests
We shall deal with
this gentleman in a
later section on
Relative Motion.
HIGHSPEED

Part 2. Cartes to Newton

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Part 2. Cartes to Newton