Galileo on Motion “ My purpose is to set forth a very new science dealing with a very ancient subject. There is, in nature, perhaps nothing older than.

Galileo on Motion

Galileo on Motion

“My purpose is to set forth a very new science dealing with a very ancient subject. There is, in nature, perhaps nothing older than motion, concerning which the books written by philosophers are neither few nor small; nevertheless I have discovered by EXPERIMENT some properties of it which are worth knowing and which have not hitherto been either observed or demonstrated.”

~ Galileo

“My purpose is to set forth a very new science dealing with a very ancient subject. There is, in nature, perhaps nothing older than motion, concerning which the books written by philosophers are neither few nor small; nevertheless I have discovered by EXPERIMENT some properties of it which are worth knowing and which have not hitherto been either observed or demonstrated.”

~ Galileo

Scientific revolution

Supporter of Copernicanism

Telescope

First and second laws of

motion

Experiment

Scientific method

“Father of modern

Astronomy”

“Father of modern physics”

“Father of science”

Freedom of thought & the

Catholic Church

LegacyLegacy

So, who’s Galileo?

Bridging the Gap: Aristotle to Galileo

Bridging the Gap: Aristotle to Galileo

Philoponus 533 A.D.

Avicenna 980 A.D.

Oresme 1330’s

Buridan

Ockham 1300’s

Born in 1564 in Pisa of Vincenzo Galilei and Guilia Ammannati Florence University of Pisa; 1581-1585 Chair of Mathematics Univ. of Pisa 1589 Father dies in 1591; Professory of Mathematics at the University

of Padua Meets Maria Gamba; Virginia (later Sister Maria Celeste) is born

(1600), Livia (1601), later Sister Arcangela, and Vincenzio (1606) 1609; the spyglass Cardinal Robert Bellarmine 1616 wrote the Letter to the Grand Duchess 1630 wrote Dialogue Concerning the Two Chief Systems of the

World Inquisition bans the Dialogue and Galileo is sentenced to lifetime

house arrest 1634 his daughter, Virginia, dies Disourses are smuggled out Died 1642

Born in 1564 in Pisa of Vincenzo Galilei and Guilia Ammannati Florence University of Pisa; 1581-1585 Chair of Mathematics Univ. of Pisa 1589 Father dies in 1591; Professory of Mathematics at the University

of Padua Meets Maria Gamba; Virginia (later Sister Maria Celeste) is born

(1600), Livia (1601), later Sister Arcangela, and Vincenzio (1606) 1609; the spyglass Cardinal Robert Bellarmine 1616 wrote the Letter to the Grand Duchess 1630 wrote Dialogue Concerning the Two Chief Systems of the

World Inquisition bans the Dialogue and Galileo is sentenced to lifetime

house arrest 1634 his daughter, Virginia, dies Disourses are smuggled out Died 1642

Galileo’s LifeGalileo’s Life

“Philosophy is written in this grand book, the universe, which stands continually open to our gaze. But the book cannot be understood unless one first learns to comprehend the language and read the characters in which it is written. It is written in the language of mathematics, and its characters are

triangles, circles, and other geometric figures without which it is humanly impossible to understand a single word of it; without these one is wandering in

a dark labyrinth.”

Galileo – from The Assayer

“Philosophy is written in this grand book, the universe, which stands continually open to our gaze. But the book cannot be understood unless one first learns to comprehend the language and read the characters in which it is written. It is written in the language of mathematics, and its characters are

triangles, circles, and other geometric figures without which it is humanly impossible to understand a single word of it; without these one is wandering in

a dark labyrinth.”

Galileo – from The Assayer

WorksWorks

De Motu (1602-1604) never published

Dialogue Concerning the Two Chief Systems of the World (1625-1630) -1632

Discourses and mathematical demonstrations concerning the two new sciences (1633-1642)-1638

De Motu (1602-1604) never published

Dialogue Concerning the Two Chief Systems of the World (1625-1630) -1632

Discourses and mathematical demonstrations concerning the two new sciences (1633-1642)-1638

Galileo’s QualifiersGalileo’s Qualifiers

Rectilinear vs. Circular Motion Straight line motion or motion parallel

with the surface of the earth? Criterion of Simplicity Agreement with experiment

Rectilinear vs. Circular Motion Straight line motion or motion parallel

with the surface of the earth? Criterion of Simplicity Agreement with experiment

Kinematics: Quantitative description of the motion of bodies

VS.Dynamics: Causes of such motion

Kinematics: Quantitative description of the motion of bodies

VS.Dynamics: Causes of such motion

Naturally Accelerated Motion/Constant

Acceleration

Naturally Accelerated Motion/Constant

Acceleration Vs. uniform motion – motion in

which equal distances are covered in equal increments of time

“A motion is said to be uniformly accelerated when, starting from rest, its speed receives equal increments in equal times”

Vs. uniform motion – motion in which equal distances are covered in equal increments of time

“A motion is said to be uniformly accelerated when, starting from rest, its speed receives equal increments in equal times”

Inclined Plane Experiments

Inclined Plane Experiments

http://brunelleschi.imss.fi.it/genscheda.asp?appl=SIM&xsl=multimed&lingua=ENG&chiave=500045

http://brunelleschi.imss.fi.it/genscheda.asp?appl=SIM&xsl=multimed&lingua=ENG&chiave=500065

http://brunelleschi.imss.fi.it/genscheda.asp?appl=SIM&xsl=multimed&lingua=ENG&chiave=500045

http://brunelleschi.imss.fi.it/genscheda.asp?appl=SIM&xsl=multimed&lingua=ENG&chiave=500065

~ 100 trials with various inclinations for various lengths of time

What do we make of this?What do we make of this?

Finds that the distance of descent always varies closely to the square of the time

Algebra had yet to be applied to such problems

The final velocity of the ball depended on how high the plane was, not directly to the plane’s incline angle

Finds that the distance of descent always varies closely to the square of the time

Algebra had yet to be applied to such problems

The final velocity of the ball depended on how high the plane was, not directly to the plane’s incline angle

Projectile MotionProjectile Motion

1. Constant downward acceleration2. Maintains constant horizontal velocity

1. Constant downward acceleration2. Maintains constant horizontal velocity

• Treat vertical and horizontal motions independently

• Combination of two components will agree with observed trajectory

•Observed trajectory is parabolic

Projectile MotionProjectile Motion

Derived Equations

Horizontal x = vot

Vertical y = 1/2gt2

Parabolic y = ( g ) x2

Trajectory 2v2o

Derived Equations

Horizontal x = vot

Vertical y = 1/2gt2

Parabolic y = ( g ) x2

Trajectory 2v2o

Projectile MotionProjectile Motion

http://brunelleschi.imss.fi.it/genscheda.asp?appl=SIM&xsl=multimed&lingua=ENG&chiave=500098

The Components of MotionThe Components of Motion

http://www.makingthemodernworld.org.uk/larning_modules/maths/04.TU.02/?section=7http://www.makingthemodernworld.org.uk/larning_modules/maths/04.TU.02/?section=7

Inertia Inertia

Momentum – product of the weight of a body times its velocity

Inertia - a body in motion tends to stay in motion (doesn’t specify straight-line)

http://id.mind.net/~zona/mstm/physics/mechanics/forces/galileo/galileoInertia.html

Momentum – product of the weight of a body times its velocity

Inertia - a body in motion tends to stay in motion (doesn’t specify straight-line)

http://id.mind.net/~zona/mstm/physics/mechanics/forces/galileo/galileoInertia.html

http://brunelleschi.imss.fi.it/genscheda.asp?appl=SIM&xsl=multimed&lingua=ENG&chiave=500135

Break from Aristotelian Philosophy?

Break from Aristotelian Philosophy?

Objects are no longer “purposeful” – break from teleology

***Disclaimer: Concepts of inertia did not begin only with Galileo

Objects are no longer “purposeful” – break from teleology

***Disclaimer: Concepts of inertia did not begin only with Galileo

Galileo on AristotleGalileo on Aristotle

Pg 84 in book and open discussion Pg 84 in book and open discussion

PisaPisa

Dropped balls diff. mass

Independent of mass

Thus, disproving Aristotle

Dropped balls diff. mass

Independent of mass

Thus, disproving Aristotle

Questions?Questions?Summary: http://brunelleschi.imss.fi.it/genscheda.asp?

appl=SIM&xsl=multimed&lingua=ENG&chiave=500012Summary: http://brunelleschi.imss.fi.it/genscheda.asp?

appl=SIM&xsl=multimed&lingua=ENG&chiave=500012

All truths are easy to understand once they are discovered; the point is to discover them.

Galileo

All truths are easy to understand once they are discovered; the point is to discover them.

Galileo