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

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 Legacy So, who’s 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;  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 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

Works  De Motu ( ) never published  Dialogue Concerning the Two Chief Systems of the World ( )  Discourses and mathematical demonstrations concerning the two new sciences ( )-1638  De Motu ( ) never published  Dialogue Concerning the Two Chief Systems of the World ( )  Discourses and mathematical demonstrations concerning the two new sciences ( )-1638

Galileo ’ 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

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 ”

Inclined Plane Experiments ~ 100 trials with various inclinations for various lengths of time

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 Motion 1.Constant downward acceleration 2.Maintains constant horizontal velocity Treat vertical and horizontal motions independently Combination of two components will agree with observed trajectory Observed trajectory is parabolic

Projectile Motion  Derived Equations  Horizontal x = v o t  Vertical y = 1/2gt 2  Parabolic y = ( g ) x 2  Trajectory 2v 2 o

Projectile Motion

The Components of Motion on=7

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)  alileo/galileoInertia.html alileo/galileoInertia.html

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 Aristotle  Pg 84 in book and open discussion

Pisa  Dropped balls diff. mass  Independent of mass  Thus, disproving Aristotle  Dropped balls diff. mass  Independent of mass  Thus, disproving Aristotle

Questions? Summary: Summary:

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