When Galileo died, his remains were awarded a great tomb - most of them!

Apparently they thought that he must have been pointing the right direction, because they kept his middle finger, which can still be seen in a museum.

They should havepaid more attention

to what was inmy head,

and what they saw with their own eyes

Hey guys. Maybe we ought to rethink this

In 1992, 359 years later, Pope Paul II acknowledged the church's error

Let’s look a little at Galileo’s mechanics. This was the other great achievement of Galileo.

And we will mention his two books:1) “The System of the World in Four Dialogues”This is a comparison of the Ptolemian and the Copernican systems.2) “Dialogues on Two New Sciences”

We’re going to do this with demonstrations.

Who is this guy “Simplicio” anyway?

1) Pendulum Experiments

2) Inclined Plane Experiments

3) Projectile motion (parabolic path)

Galileo used simple ways of measuring timewater clocks.

Named clepsydras ("water thief” by the Greeks, who began using them about 325 B.C., these were stone vessels with sloping sides that allowed water to drip at a nearly constant rate from a small hole near the bottom. Other clepsydras were cylindrical or bowl-shaped containers designed to slowly fill with water coming in at a constant rate. Markings on the inside surfaces measured the passage of "hours" as the water level reached them.

Siphon Water Clock

Persistence of Memoryby Salvador Dali

Keeping time was important, and

water clocks were used before the

pendulum clocks

In 1656, Christiaan Huygens, a Dutch scientist, made the first pendulum clock, regulated by a mechanism with a "natural" period of oscillation. Although Galileo Galilei, sometimes credited with inventing the pendulum, studied its motion as early as 1582, Galileo's design for a clock was not built before his death. Huygens' pendulum clock had an error of less than 1 minute a day, the first time such accuracy had been achieved. His later refinements reduced his clock's errors to less than 10 seconds a day.

Who discovered the pendulum

clock?

I did!

This is a copy of the original diagram made by Vincenzo Viviani and Galileo's son, Vincenzo. It is mounted in an oval frame whose feet and frieze are gilded. It embodies the idea described by Galileo in a letter written to the Dutch scholar Lorenzo Realio in June 1637. Galileo explained to Realio the method he had in mind to determine longitude at sea and on land by observing the periods of the satellites of Jupiter. This operation required a precise measurement of time and Galileo mentioned that he had invented a clock that was so precise that it could determine very small intervals of time anywhere, without any error whatsoever and in any season of the year. The accuracy of this clock depended on the isochronism of the oscillations of pendulums of equal length which Galileo had demonstrated in his research in the field of mechanics. The discovery of this mechanism and the role played by Vincenzo Galilei is described in a lengthy account by Viviani in his Racconto Istorico of the life of Galileo. In 1658 Christiaan Huygens claimed that he had discovered how to apply the pendulum to timing devices but his claim was hotly contested by Viviani.

Actually I thought of it already

Lectures are not what they used to be

This is the chair from which Galileo gave his lectures

Script where Galileo talked about the satellites of Jupiter

I think we will stickto other things

http://www.its.caltech.edu/~newman/sci-cp/sci-9211.html

http://es.rice.edu/ES/humsoc/Galileo/Student_Work/Trial96/index.html

Read about it here

Woops!

The earthdoes move!

Retraction!

Nineteenth century. Tito Lessi.

This painting depicts the aged Galileo with Vincenzo Viviani, his last disciple. In 1639, when he was seventeen years old, Viviani went to stay with Galileo whom he worked with until the death of the great scientist in 1642.

Monument at Galileo’s Tomb

Galileo and Viviani

The remains of Galileo were moved to this spot on 12 March 1737, the date on which the index finger of his right hand was removed.

Several years ago the Testator ordered that a marble statue be made of the face and bust of that incomparable philosopher, geometer and astronomer, Galileo Galilei, the Noble Florentine. He intended to place it in the Church of Santa Croce in this City, and to bury under the bust the bones of his venerated Master that are now in the Novitiate of the Conventual Friars of the Church of Santa Croce. He also wished that a suitable epitaph in marble be placed to record the admirable discoveries that Galileo made in the heavens and on earth. If during his life the Testator was unable to fulfil this intention, which was motivated by a feeling of gratitude towards so great a Master, he asks that his wish be fulfilled after his death at the order and expense of his executors. He asks that his own body be placed in the Church of Santa Croce under the statue of the great Galileo, next to or under his bones after they have been transported to that place. If Galileo's bones are not yet in the Church, the Testator asks that his own body be placed close to that of Galileo. The Testator requests that what he has stipulated be fulfilled according to the plan of Giovanni Battista Foggini, the celebrated Florentine sculptor and dear friend of the Testator.

Will of Vincenzo Viviani

grave where Galileo is buried in Santa Croce Church in Florence, Italy

L L

A a

Interesting facts about a pendulum swing

Does the frequency of the oscillation depend on the amplitude of the swing?This was what Galileo noticed about the swinging of the chandelier.

A A

L L

Does the frequency of the oscillation depend on the size (mass) of the pendulum.Remember Galileo did not really know, or understand the ramifications about the mass.

A/2

LL

h ?

If an object (acting as a thin post) is inserted into the way of the string of the pendulum, how high does the ball rise? What does this mean?

We’e gonna have ta’wait for this one!

s

h

s

time

v

time

These are the curves we want to investigate.

Does it depend on the shape of the object?

Galileo’s inclined plane

s

h

No friction

Does this make a difference if it does not roll?

Start: give an initial “x” velocity; no initial “y” velocity

floor

123 0

What is the path of the red balls ?

x

h

Projectile motion (parabolic path)

y

How long does it take the different balls to drop to the floor?

We will do the “shoot the monkey” experiment.

Here is a page from one of Galileo's manuscripts in which he writes down the

figures he obtained in performing this experiment himself.

MEASURE! QUANTIFY!

This illustration reflects the general opinion before Galileo which followed largely Aristotelian lines but incorporating as well a later theory of "impetus" -- which maintained that an object shot from a cannon, for example, followed a straight line until it "lost its impetus," at which point it fell abruptly to the ground.

Later, simply by more careful observation, as this illustration from a work by Niccolo Tartaglia clearly shows, it was realized that projectiles actually follow some sort of a curved path

It was another essential insight that led Galileo, finally, to his most remarkable conclusion about projectile motion. First of all, he reasoned that a projectile shot from a cannon is not influenced by only one motion, but by two -- the motion that acts vertically is the force of gravity, and this pulls the projectile down by thetimes-squared law. But while gravity is pulling the object down, the projectile is also moving forward, horizontally at the same time. And this horizontal motion is uniform and constant according to his principle of inertia.

Number, Weight and Measure

Galileo got his ideasby making experiments:independent coordinates

Riccioli's dramatic depiction of the hand of God, creating the world according to mathematical principles.

"Many will pass through and knowledge will be increased."

Frontispiece to Francis Bacon's great work, the Instauratio Magna, 1620; sailing through the Pillars of Hercules;"True Direction Concerning the Interpretation of Nature."

exploration of the world depends upon observation using scientific instruments

-- as well as mathematics

iconography of an atlas by Marco Coronelli

Where are the limits of man's possible exploration?

Close relation between the Renaissance

artists and the new discoveries

that science

Shooting the Monkey(tranquilizer gun)

Where does the zookeeper aim if he wants to hit the monkey?

( He knows the monkey willlet go as soon as he shoots ! )

See text: 4-3

See examples 4-3 and 4-6

The next slides are taken from Physics 111 lecture notes

Shooting the Monkey...

See text: 4-3

If there were no gravity, simply aim

at the monkey

r = r0

r =v0t

Shooting the Monkey...

rr = vv0 t - 1/2 gg t2

See text: 4-3

With gravity, still aim at the monkey! rr = r0 - 1/2 gg t2

Dart hits the monkey!

Recap:Shooting the monkey...

x x = = xx00

yy = -1/2 gg t2

This may be easier to think about ,

It’s exactly the same idea!!

See text: 4-3

xx = = vv0 0 tt

yy = -1/2 gg t2

Was’ he talkin’ about? NOW - we’re ready for Newton!Yeah! - ???

Remember to hand in the problem set #2 on Monday (February 12)Remember to hand in the problem set #3 on Monday (February 19)

There is the first hour exam on February 19, during the class time. Bring your class notes - it is an “open notes” exam.The topics covered up to today will be on the exam.

Remember to be thinking about your semester report. It is only due at the end of the semester,

but you will probably want to be working on it earlier

Next time we start with Newton. This will not be on the exam.