Part 1. world in motion

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THE WORLD IN MOTION

Motion in the Observable World
In daily life motion is evident when things are moving. Everywhere we see: people
move; birds fly. In the cosmos, the sun and moon rise and fall; planets twirl around
stars; galaxies whistle through space.
Time moving
Birds
moving
Earth moving Sun moving
Galaxies moving
Man
moving

Motion in the Microscopic World
Not only that, it has been proven beyond doubt that all the small material bodies in this
universe are in a state of motion: molecules vibrating; electrons orbit around nuclei;
neutrinos fly in every direction; quarks and gluons twitching inside the elementary
particles.
Cells moving
Molecules moving
Atoms moving Quarks moving

Definition of Motion
The word ‘motion’ came from the Greek word ‘motus’ which means change. In ancient
Greece, motion includes fluxes, growths, meltings, coolings, heatings . . . etc. The
ancient Greek philosophers recognized that the world is transient and is constantly
changing.

Translational Motion
To be more precise and scientific in physics, by motion we mean the change of position
in space, that is, ‘translational motion’.
Translation
al motion
Changes

Speed
In translational motion, speed is the perception of how fast an object moves. The
concept is a simple one and was well known in the early civilizations or even in
prehistoric times. In fact it is so simple that its origin is never noticed.
Slow = Low Speed Fast = High Speed

Ancient Greeks on Speed
Serious consolidation of the concept of motion may have been started with the ancient
Greek philosophers when they began to ponder upon the phenomenon of objects in
motion.
For example, the great philosopher Aristotle (384–322 BC) had his own notion of
motion in that time is proportional to the distance moved. He said:
“For at any moment when a thing is causing motion, it also has caused motion, so that
there must always be a certain amount of distance that has been traversed and a
certain amount of time that has been occupied.” Aristotle’s Physics VII.
The idea of speed

Galileo’s Investigation
It was probably Galileo Galilee (1564-1642) who first developed the conception of
motion in definite and quantitative terms. Through his various investigations such as
the slide experiment, he used the mathematical notion of velocity as distance over a
period of time.
Dripping water
to count time
Ball rolling
down slide
Slide tilted to have
different angles
𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉
= 𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 ÷ 𝑇𝑇𝑇𝑇 𝑇𝑇𝑇𝑇

Units of Distance & Time
Distance and time are two independent
quantities, each with their own measurement
units. Distances are measured in cm, m, km etc.,
in the metric system and inches, feet, miles in the
imperial system. For convenience, the metric
system is used throughout in our discussions with
imperial units in brackets if necessary.
Time is more universal. It is measured in seconds,
minutes, hours, days, etc. which we are familiar
with.
Distance units in cm, m, km, etc.
Time units in second, minutes
Hours, days, etc

Equation for Velocity
For the special case of uniform motion in
which an equal distance (∆𝑥𝑥 =
𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑) is covered in equal interval of
time (∆𝑡𝑡 = 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡), it can be written as:
𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈 𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉 𝑣𝑣
= 𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 (Δ𝑥𝑥) ÷ 𝑇𝑇𝑇𝑇 𝑇𝑇𝑇𝑇 Δ𝑡𝑡
Or simply in pure mathematical form:
𝑣𝑣 =
Δ𝑥𝑥
Δ𝑡𝑡
𝒗𝒗
=
𝜟𝜟𝜟𝜟
𝜟𝜟𝜟𝜟

Geometric Representation of Speed
Since distance (space) and time are
two independent quantities, we
can represent them by the two
perpendicular coordinates of a
Cartesian coordinate system: y-
axis take up distance and x-axis
looks after time. Velocity become
the slanting line or slope across
space and time.
Thus speed is measured by meters
or feet per second, kilometres or
miles an hour.
By interposing, we have the
distance:
Δ𝑥𝑥 = 𝑣𝑣Δ𝑡𝑡
Distance(space)
Time
Δ𝑥𝑥
Δ𝑡𝑡
𝑣𝑣 =
Δ𝑥𝑥
Δ𝑡𝑡

The Kinematic Piece
Galileo’s kinematics was accepted by physicists in the subsequent centuries and
became the basis of Newton’s work and the foundation of classical mechanics.
Velocity

THE CAUSE OF MOTION IN ANCIENT GREECE

What makes a thing move?
With things in motion, there comes the question of what makes an object move. Why
do things fall? Who sets the heavenly bodies in motion? What is done on an object to
make it achieve a velocity?

It Started with the Greeks
Normally the average person would not have concerned with such a question. Motion
is natural. We walk from one location to another; we push and pull so as to make an
object move; the sun rises and falls . . . But the ancient Greeks did not stop at that.

Aristotle Physics
The first comprehensive &
systematic set of ideas about the
physical world was developed by
the great Greek philosopher
Aristotle (384–322 BC) in the
fourth century BC. It is often
referred to as Aristotelian
physics and the concept of a
force is an integral part of
Aristotelian cosmology.
Aristotle & his geocentric universe

Observations by Aristotle
Aristotle is a genius with very sharp
observation and keen analytic power.
However he was heavily handicapped
because he did not have the notion of
experimental instruments to carry
them out. Neither did he has the
correct concept of gravitation or the
force of friction to start with. This is
why he often made astounding but
erroneous assumptions which led to
complicated but also erroneous
deductions. He can be considered as a
genius with two heads like the god
Janus but with one of them blind.
Blind

Celestial Motion
Aristotle did observe that:
❶ The stars and heavenly bodies circulate
permanently around the earth as if moved by
angel or god.
According to modern mechanics, celestial
motion is the combined effect of linear motion
and gravitation. Aristotle did not understand the
interaction of gravitation and linear motion and
came to the notion that motion is initiated by
angels or god himself who decreed that the
heavenly bodies should circulate permanently
around the earth.
We leave celestial motion to the discussion on
circular and orbital motions of celestial objects
for later.

Gravitational Motion
❷ Things that have gone up will come
done naturally towards the centre of the
earth. Example is the fall of Icarus when
his wings were melted by the heat of the
sun as he went far too high and too close
to the sun.
We know that this motion is rectilinear
and is caused by the force of gravity.
Aristotle did not understand these and so
made such a classification.
This class of motion is to be studied in our
discussions on gravitation.

Forced Motion
❸ Things on earth move because the
application of force. So they are called forced
or unnatural motion by Aristotle.
This is the class of motions we are familiar
with in our daily life. They are always
interpreted as our bodily effort of a push or a
pull.
However Aristotle also observed that things
on earth will stop moving in the absence of
continuous force application. He did not
know that it is actually friction that is
working against the motion.
This is the misconception that acts as the
prelude to our present discussion.
Force Friction
Forced motion
No motion

Motions with Movers
Aristotle concluded with the
assumption that an object cannot
move by itself because every
movement depends on there
being a mover – some body is
needed to push or pull them.
Mover
Moved
Mover

Problem with Projectiles
But what about projectiles?
They don’t obey Aristotle’s rule because
they keep on moving after leaving the
thrower or bow without the need of
further force applied to them.

Air Behind Projectile Motions
Aristotle maintained that after leaving the shooter’s bow, the arrow still continues to
move because a new force is still transmitted to the arrow through a medium such as
air. It is the air closing in behind a moving arrow propelled it so that it will keep on
moving until it drops.
❸
Air turns around and pushes
the projectile forward.
❶ Air being pushed
forward by stone in front
and so turns back.
❷ Air flows to the side
and then back of the stone.

Cannon Ball Trajectory
Thus according to Aristotle, a cannon ball will
shoot up straight at first and then drops dead
straight to the ground.
A medieval drawing showing cannon ball
trajectory.

Medieval Age
The Middle Ages in European
history lasted from the fall of
the western Roman Empire
(circa A.D. 395) to the
Renaissance in the 14th or
15th century. During this
period, the civilisation of the
Greeks and Romans were
replaced by barbarism. Most
of the ancient teachings and
their records were lost or
destroyed. Fortunately ome
of them were copied and
preserved in the Muslim
countries.
The devastation of Greek and Roman civilizations

Revival of Greek Learnings
From the thirteenth century onward
these writings came to see the light again
in Europe. They were recovered as rare
copies from forgotten corners in the attic
or store rooms. Some of them were also
brought back from the Muslim countries
translated in Latin. After emerging from a
thousand years of darkness, the European
civilisation was in a badly retrograded
shape. The ancient knowledge and
philosophies appeared so far superior to
theirs that they were treated with almost
superstitious reverence. The teaching of
Aristotle in particular became the guiding
light of the time.

Authority of Aristotle’s
Teachings
The weight of Aristotle's teachings were
later further enhanced by St. Thomas
Aquinas (1224-1274 B.C.) who brought
them in line with the Bible, making them
the answer books to all scientific
enquiries.
In the centuries to come Aristotle's
philosophy was regarded as the ultimate
truth throughout Europe. When Aristotle
said that a heavy rock falls faster than a
lighter one, no one else would have
thought otherwise.

John Philoponus
The Aristotelian theory of forced
motion encountered criticism in the
Medieval age, first and formally by
John Philoponus in the 6th century.
Philoponus (AD 490-570) in Greek
means "lover of work“. He was so
called because he spent most of his
time studying.
He was an Alexandrian Christian
who disagreed with Aristotle's
philosophy.
One of his most important
achievements in spear heading
Alexandria’s science was his theory
of impetus.

Philoponus’ major argument against Aristotle was on the cause of motion. He opposed to the idea of
a medium of force such as air because it would resist the motion of a projectile and definitely could
not also propel that projectile.
The Medium of Force
Projection motion
Air resistance

Motive Cause - Impetus
Philoponus believed that a stone moved because something like a force had impressed
onto it. The stone absorbed the force, moved a little faster and continued to move on.
It eventually had to cease motion because of encountering situations such as resistance
from the air or collision with another body. The cause of movement or the motive
force, Philoponus concluded, resided within the stone itself. He called this something
‘impetus’.
BEFORE
AFTER Impetus

Eternal Celestial Motions
As for the celestial movements Aristotle attributed them to the power of spirits. But
Philoponus suggested that the Creator had impressed movement upon the original
universe in the first place and the universe went on with the momentum impressed
on it. In the same manner as the stone projectile, once the cause of motion was
imparted, an object in a void would keep on going because of impetus, without any
further push.

Breaking the Earth-Heaven Barrier
This endowment by God did not
decay with time. So it was no longer
necessary to postulate a variety of
angelic movers working on the
heavenly bodies.
This is in the truth of the law of
conservation of impetus though
Philoponus did not explicitly
recognized it.
This conception, besides establishing
impetus as a individually existing
entity, it was also a major step in
breaking down the difference
between the movement of heavenly
and earthly objects as conceived by
Aristotle.

Philoponus vs Aristotle
To Aristotle, motion is an effect
caused by an external agent – an
external force. In Philoponus’
theory, motion is an intrinsic
property of the moving object
itself. Impetus, the driving agent,
is first imparted to an object and
set the object in motion and later
abides within the moving object
on its journey.
This is for the first time in a
thousand years when the ideas of
Aristotle were seriously and
challenged and gain acceptance.

What is the Nature of Impetus?
Impetus seems to be something that exists naturally in this world. It appears to
Philoponus that it is a fundamental fact of nature and did not give further elaboration
on it.
?

The Impetus Piece
Understood or not, we have been able to
obtain another important piece for our
motion puzzle after velocity – impetus.
Velocity
Impetus

JEAN BURIDAN
The Renegade Monk

Jean Buridan
Jean Buridan (1295-1358) was a
French priest credited to be the
person who sowed the seeds for
the Copernican revolution in
Europe.
Before Buridan, natural philosophy
was only a handmaiden of
theology or a mere disciple after
the doctrines of Aristotle. After the
time of Buridan, it began to have
its own legitimacy and developed
in a new direction.

Motion of Projectiles
Like Philoponus in the 6thcentury, Buridan was particularly in discordance with
Aristotle’s concept on motion of projectiles.
The trajectory of a projectile by Aristotle

Buridan on Projectiles
Buridan said: “. . . after leaving the arm of the thrower, the projectile would be moving
by an ‘impetus’ given to it by the thrower and would continue to move as long as the
impetus remained stronger than the resistance, and would be of infinite duration were
it not diminished and corrupted by a contrary force resisting it or by something
inclining it to a contrary motion.”
IMPETUS

Buridan’s Impetus
According to Buridan in his “Quaestiones on
Aristotle's Physics”:
“When a mover sets a body in motion he
implants into it a certain impetus:
[𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 = 𝐼𝐼 𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼]
. . . a certain force enabling a body to move in
the direction in which the mover starts it, be it
upwards, downwards, sidewards, or in a circle.
[𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 𝑜𝑜𝑜𝑜 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 =
𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 𝑜𝑜𝑜𝑜 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖]

Buridan’s Equation
The implanted impetus increases in
the same ratio as the velocity.
[𝐼𝐼 𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼 ∝ 𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉]
in fact, Buridan gave it a
mathematical formulation:
𝐼𝐼 𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼 = 𝑊𝑊𝑊𝑊𝑊𝑊𝑊𝑊𝑊𝑊𝑊 × 𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉
The weight is a constant that does not
change. So the impetus is purely a
function of velocity. Faster object has greater impetus

INERTIA
Impetus became Momentum
It can be said that what Buridan did was very close to defining momentum in the
Newtonian sense 𝒑𝒑 = 𝑚𝑚𝒗𝒗.
This impetus theory was revived in the thirteenth century by Peter John Olivi (c. 1248-
1298) and has been incorporated into modern physics as momentum.
Buridan’s IMPETUS

Nature of Impetus
Apparently Buridan’s way of thinking was on the right track. But again like Philoponus,
he did not investigate further why it should be as he thought. It seemed to him that it
was an elementary fact and resumed no further explanation. What is impetus? What is
in impetus that is passed on from one body to another to make a body move?
IMPETUS
?
To be continued in Part 2.

Part 1. world in motion

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Part 1. world in motion