galileo pendulum experiment

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Galileo Galilei The Law of the Pendulum

 Italian mathematician, astronomer, physicist and inventor Galileo Galilei lived from 1564 to 1642. Galileo discovered the "isochronism of the pendulum" aka the "law of the pendulum". Galileo demonstrated at the Tower of Pisa that falling bodies of different weights descend at the same rate. He invented the first refracting telescope, and used that telescope to discover and document Jupiter's satellites, sunspots, and craters on the Earth's moon. He is considered to be the "Father of the Scientific Method".

• Complete Biography of Galileo Galilei
• Galileo Galilei Quotes

The painting above depicts a  young twenty year old Galileo observing a lamp swinging from a cathedral ceiling. Believe it or not Galileo Galilei was the first scientist to observe how long it took any object suspended from a rope or chain (a pendulum) to swing back and forth. There were no wrist watches at that time, so Galileo used his own pulse as a time measurement. Galileo observed that no matter how big the swings were, as in when the lamp was first swung, to how small the swings were as the lamp returned to a standstill, the time it took for each swing to complete was exactly the same.

Galileo Galilei had discovered the law of the pendulum, which gained the young scientist considerable notoriety in the academic world. The law of the pendulum would later be used in the construction of clocks, as it could be used to regulate them.

Proving Aristotle Was Wrong

While Galileo Galilei was working at the University of Pisa, there was a popular discussion occurring about a long dead scientist and philosopher called Aristotle . Aristotle believed that heavier objects fell faster than lighter objects. Scientists in Galileo's time still agreed with Aristotle. However, Galileo Galilei did not agree and set up a public demonstration to prove Aristotle wrong.

As depicted in the illustration above, Galileo used the Tower of Pisa for his public demonstration. Galileo used a variety of balls of different sizes and weights, and dropped them off of the top of the Tower of Pisa together. Of course, they all landed at the same time since Aristotle was wrong. Objects of different weights all fall to earth at the same speed.

Of course, Gallileo's smug reaction to being proven right won him no friends and he was soon forced to leave the University of Pisa.

The Thermoscope

By 1593 after his father's death, Galileo Galilei found himself with little cash and lots of bills, including the dowry payments for his sister. At that time, those in debt could be placed in prison.

Galileo's solution was to start inventing in hopes of coming up with that one product which everyone would want. Not much different from the thoughts of inventors today.

Galileo Galilei invented a  rudimentary thermomete r called the thermoscope, a thermometer which lacked a standardized scale. It was not a big success commecially.

Galileo Galilei - Military and Surveying Compass

In 1596, Galileo Galilei made headway into his debtor's problems with the successful invention of a military compass used to accurately aim cannonballs. A year later in 1597, Galileo modified the compass so that it could be used for land surveying. Both inventions earned Galileo some well-needed cash.

Galileo Galilei - Work With Magnetism

The photo above is of the armed lodestones, used by Galileo Galilei in his studies on magnets between 1600 and 1609. They are made of iron, magnetite and brass. A lodestone by definition is any naturally magnetized mineral, able to be used as a magnet. An armed lodestone is an enhanced lodestone, where things are done to make the lodestone a stronger magnet, such as combining and placing additional magnetic materials together. 

Galileo's studies in magnetism began after the publication of William Gilbert's De Magnete in 1600. Many astronomers were basing their explanations of planetary motions on magnetism. For example Johannes Kepler , believed that the Sun was a magnetic body, and the motion of the planets was due to the action of the magnetic vortex produced by the Sun's rotation and that the Earth's ocean tides were also based on the magnetic pull of the moon.

Gallileo disagreed but never the less spent years conducting experiments on magnetic needles, magnetic declination, and the arming of magnets.. 

Galileo Galilei - First Refracting Telescope

In 1609, during a holiday in Venice Galileo Galilei learnt that a Dutch spectacle-maker had invented the spyglass ( later renamed the telescope ), a mysterious invention that could make distant objects appear closer.

The Dutch inventor had applied for a patent, however, much of the details surrounding the spyglass were being kept hush-hush as the spyglass was rumored to hold a military advantage for Holland.

Galileo Galilei - Spyglass, Telescope

Being a very competitive scientist, Galileo Galilei set out to invent his own spyglass, despite never having seen one in person, Galileo only knew what it could do. Within twenty-four hours Galileo had built a 3X power telescope, and later after a bit of sleep built a 10X power telescope, which he demonstrated to the Senate in Venice. The Senate praised Galileo publicly and raised his salary.

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• The History of Money
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• 13 Unexpected Leap Year Facts
• Biography of Charles Wheatstone, British Inventor and Entrepreneur

Galileo's Pendulum Experiments

Misconceptions

• Classroom Physics

Galileo's pendulum

Galileo was interested in predicting how bodies move. He allowed an object to roll down and up a curved track, and showed that it rose to roughly the height from which it was released, regardless of the shape of the track.

Galileo recognized that, unfortunately, the experiment was marred by the effects of friction.

Experiment: Demonstrate Galileo's rolling ball

Scientists seek to demonstrate phenomena clearly. They try to eliminate any undesired external influences (in this case, friction), in order to show an underlying principle.

Galileo's rolling ball

Galileo went on to use a pendulum to demonstrate the same phenomenon. He believed that this would be even less affected by friction.

Experiment: Set up a simple pendulum

Demonstrate how it swings.

• the effect is probably not noticeable from one swing to the next.

Experiment: Demonstrate Galileo's pin and pendulum

Galileo's pin and pendulum

In fact, the idea of the conservation of energy was far in the future when Galileo described and explained his experiment. Instead, he talked in terms of momento and impeto. These terms correspond (more or less) to what is now called momentum.

Later, Newton also used the idea of momentum, which he regarded as the fundamental property of a moving object. The idea of kinetic energy was not established until the mid-19th century, 200 years after Galileo's death.

Ideas like that of energy, which scientists today take for granted, are not self-evident. Both momentum and kinetic energy were identified when people realized that they were conserved quantities in certain situations.

Acknowledgement

We are grateful to David Sang, author of this Case Study.

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• > Journals
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• > A phenomenology of Galileo's experiments with pendulums

Article contents

A phenomenology of galileo's experiments with pendulums.

Published online by Cambridge University Press:  21 July 2009

The paper reports new findings about Galileo's experiments with pendulums and discusses their significance in the context of Galileo's writings. The methodology is based on a phenomenological approach to Galileo's experiments, supported by computer modelling and close analysis of extant textual evidence. This methodology has allowed the author to shed light on some puzzles that Galileo's experiments have created for scholars.

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1 Galileo to Guido Ubaldo dal Monte, Padua, 29 November 1602, in Galileo, Le opere di Galileo Galilei: Edizione Nazionale (ed. A. Favaro), 20 vols., Florence, 1890–1909, x, 97–100, translated in P. Palmieri, Reenacting Galileo's Experiments: Rediscovering the Techniques of Seventeenth-Century Science , Lewiston, NY, 2008, 257–60. ‘Isochronism’ is the property of certain physical systems to oscillate at constant frequency regardless of the oscillations' amplitude. We now know that simple pendulums are not isochronous. ‘Isochronism’ is not a Galilean word. As the reader will see, Galileo uses other expressions to refer to this property. I will retain ‘isochronism’ since it has become common in the literature.

2 Koyré , A. , ‘ An experiment in measurement ’, Proceedings of the American Philosophical Society ( 1953 ), 97 , 222 –37 Google Scholar ; P. Ariotti, ‘Galileo on the isochrony of the pendulum’, Isis (1968), 59 , 414–26; idem , ‘Aspects of the conception and development of the pendulum in the 17th century’, Archive for History of Exact Sciences (1972), 8 , 329–410; Drake , S. , ‘ New light on a Galilean claim about pendulums ’, Isis ( 1975 ), 66 , 92 –5 CrossRef Google Scholar , reprinted in idem , Essays on Galileo and the History and Philosophy of Science , 3 vols., Toronto, 1999, ii, 316–20; idem , Galileo: Pioneer Scientist , Toronto, 1990, 9 ff.; idem , Galileo at Work: His Scientific Biography , New York, 1995 (1st edn Chicago, 1978), 69–70; Naylor , R. , ‘ Galileo's simple pendulum ’, Physis ( 1974 ), 16 , 23 – 46 Google Scholar ; idem , ‘Galileo's need for precision: the point of the Fourth Day pendulum experiment’, Isis (1977), 68 , 97–103; idem , ‘Galileo, Copernicanism and the origins of the new science of motion’, BJHS (2003), 36 , 151–81; MacLachlan , J. , ‘ Galileo's experiments with pendulums: real and imaginary ’, Annals of Science ( 1976 ), 33 , 173 –85 CrossRef Google Scholar ; Costabel , P. , ‘ Isochronisme et accélération 1638–1687 ’, Archives internationales d'histoire des sciences ( 1978 ), 28 , 3 – 20 Google Scholar ; Hill , D. , ‘ Pendulums and planes: what Galileo didn't publish ’, Nuncius ( 1994 ), 9 , 499 – 515 CrossRef Google Scholar ; T. Settle, ‘La rete degli esperimenti Galileiani’, in Galileo e la scienza sperimentale (ed. M. Baldo Ceolin), Padua, 1995, 11–62; Machamer , P. and Hepburn , B. , ‘ Galileo and the pendulum: latching on to time ’, Science & Education ( 2004 ), 13 , 333 –47 CrossRef Google Scholar ; Matthews , M. , ‘ Idealisation and Galileo's pendulum discoveries: Historical, philosophical and pedagogical considerations ’, Science & Education ( 2004 ), 13 , 689 – 715 . CrossRef Google Scholar

3 Naylor, ‘Galileo's simple pendulum’, op. cit. (2), 23.

4 Naylor, ‘Galileo's simple pendulum’, op. cit. (2), 23. The Discorsi referred to by Naylor are the Two New Sciences .

5 Hill, op. cit. (2), 513. Hill's conclusion is untenable: I have suggested a counterargument based on a repetition of Galileo's calculations concerning the so-called brachistochrone, on which Hill's indictment hinges, in Palmieri, op. cit. (1), 248–55.

6 MacLachlan, op. cit. (2), 173.

7 A. Koyré, Études Galiléennes , Paris, 1966 (1st edn 3 vols., Paris, 1939).

8 Costabel, op. cit. (2), 6. Costabel doubts that Galileo could have done the experiments with cork and lead pendulums since in his view Galileo's reasoning about the experiment is erroneous. Costabel's argument only shows his misunderstanding of what Galileo's experiments with cork and lead pendulums are really about and their function as evidence (see below, ‘A crucial experiment in the historiography of isochronism’).

9 Naylor, ‘Galileo's simple pendulum’, op. cit. (2). Settle's groundbreaking reconstruction of the inclined plane experiment takes a different approach and carefully avoids the trap of the matching problem. Settle , T. , ‘ An experiment in the history of science ’, Science ( 1961 ), 133 , 19 – 23 . CrossRef Google Scholar PubMed

10 Belloni , L. , ‘ The repetition of experiments and observations: its value in studying the history of medicine (and science) ’, Journal for the History of Medicine and Allied Sciences ( 1970 ), 25 , 158 –67 CrossRef Google Scholar ; and Belloni's commentaries in M. Malpighi, Opere scelte (ed. L. Belloni), Turin, 1967. In recent years, more scholars have embraced an experimental approach to the history and philosophy of this science: for instance, Settle, op. cit. (9); Wilson , C. , ‘ Re-doing Newton's experiment for establishing the proportionality of mass and weight ’, St John's Review ( 1999 ), 45 , 64 – 73 Google Scholar ; J. Renn and P. Damerow, ‘The hanging chain: a forgotten “discovery” buried in Galileo's notes on motion’, in Reworking the Bench: Research Notebooks in the History of Science (ed. F. Holmes, J. Renn and H.-J. Rheinberger), New York, 2003, 1–24.

11 Naylor, ‘Galileo's simple pendulum’, op. cit. (2).

12 Naylor, ‘Galileo's simple pendulum’, op. cit. (2), 38–9.

13 See Palmieri, op. cit. (1), 217, for the mathematical details.

14 Galileo to Guido Ubaldo dal Monte, 29 November 1602, Edizione Nazionale , op. cit. (1), x, 97–100, and Palmieri, op. cit. (1), 257–60; Galileo, Dialogue on the Two Chief World Systems (1632), Edizione Nazionale , vii, 256–7, 474–6, and Palmieri, op. cit. (1), 260–2, 262–3; Two New Sciences (1638), Galileo, Edizione Nazionale , viii, 128–9, 139–40, 277–8, and Palmieri, op. cit. (1), 263–4, 264–5, 265–8.

15 Hemp is a material that would have been easily available in Galileo's time. Linen would also have been available. Galileo says spago or spaghetto , i.e. thin string, which implies that the string's material would probably have been hemp or linen. See the ‘Supporting document’ for further details.

16 The choice of the lead balls is somewhat problematic. Galileo does not specify the size of the lead balls he uses, but the words he chooses seem to indicate that he used very small balls, roughly the size of musket balls, or little more. Musket balls at that time would have been in the range of one to two ounces (between about twenty-eight and fifty-six grams). See ‘Supporting document’ for further details.

17 Galileo to Guido Ubaldo dal Monte, 29 November 1602, Edizione Nazionale , op. cit. (1), x, 97–100, and Palmieri, op. cit. (1), 257–60; Galileo, Two New Sciences (1638), Edizione Nazionale , viii, 128–9, 277–8, and Palmieri, op. cit. (1), 263–4, 265–8. I will consistently use ‘oscillation’ to indicate a complete swing of the pendulum, back and forth from starting point to maximum height on the other side with respect to the perpendicular and return. Galileo's language is not always clear when referring to pendulum swings, at times suggesting oscillations, other times perhaps half oscillations.

18 This is how I performed the adjustment of the lengths of the pendulums. It is, of course, possible to think up better fine-tuning methods, but they are trial-and-error procedures, since the lengths of the pendulums will always look the same all the time (obviously within the limits of technologies that would have been available to Galileo).

19 See the ‘Supporting document’; and also Palmieri, op. cit. (1), Appendix 1.

20 Galileo, Dialogue on the Two Chief World Systems (1632), Edizione Nazionale , op. cit. (1), vii, 256–7, and Palmieri, op. cit. (1), 260–2.

21 For a description of the thin string see Galileo, Two New Sciences (1638), Edizione Nazionale , op. cit. (1), viii, 128–9, and Palmieri, op. cit. (1), 263–4.

22 Galileo to Guido Ubaldo dal Monte, 29 November 1602, Edizione Nazionale , op. cit. (1), x, 97–100, and Palmieri, op. cit. (1), 257–60; Galileo, Two New Sciences (1638), Edizione Nazionale , op. cit. (1), viii, 128–9, and Palmieri, 263–4.

23 Braun , Cf. M. , ‘ On some properties of the multiple pendulum ’, Archive of Applied Mechanics ( 2003 ), 72 , 899 – 910 Google Scholar , for a discussion of a multiple-mass pendulum model. I have adopted Braun's linear approximation for my hundred-mass model of the chain pendulum.

24 Galileo, Dialogue on the Two Chief World Systems (1632), Edizione Nazionale , op. cit. (1), vii, 474–6, and Palmieri, op. cit. (1), 262–3.

25 Galileo, Dialogue on the Two Chief World Systems (1632), Edizione Nazionale , op. cit. (1), vii, 256–7 and Palmieri, op. cit. (1), 260–2.

26 Galileo to Guido Ubaldo dal Monte, 29 November 1602, Edizione Nazionale , op. cit. (1), x, 97–100, and Palmieri, op. cit. (1), 257–60.

27 Galileo, Edizione Nazionale , op. cit. (1), viii, 205–8.

28 It is rather easy to cast lead balls since lead's liquefying temperature is not too high. It is therefore possible that Galileo would have cast his own lead balls, in which case he would have been free to cast balls of different weights than musket balls (see the ‘Supporting document’ for more on lead balls and other materials).

29 Galileo to Guido Ubaldo dal Monte, 29 November 1602, Edizione Nazionale , op. cit. (1), x, 97–100, and Palmieri, op. cit. (1), 257–60.

30 At one point in the course of the experiments, the impression emerged that the two pendulums might somehow interfere with each other. The possible effects of interference are discussed later in this section. The two pendulums did not interfere in any appreciable way. I tested this conclusion by leaving one of the two pendulums at rest and operating the other to see if the motion of one might excite some movement in the other. Video 8 (‘The stability of the pendulum’) shows that the pendulum left at rest remains at rest while the other oscillates for a long period of time, well beyond the four to five minutes of the time window allowed.

31 Galileo to Guido Ubaldo dal Monte, 29 November 1602, Edizione Nazionale , op. cit. (1), x, 97–100, and Palmieri, op. cit. (1), 257–60; Galileo, Two New Sciences (1638), Edizione Nazionale , viii, 277–8, and Palmieri, op. cit. (1), 265–8.

32 Galileo, Two New Sciences (1638), Edizione Nazionale , op. cit. (1), viii, 277–8, and Palmieri, op. cit. (1), 265–8.

33 In Two New Sciences (1638), Edizione Nazionale , op. cit. (1), viii, 277–8, Galileo seems to argue that the count would disagree not only by not even one oscillation, but also by not even a fraction of one oscillation, and for angles up to more than eighty degrees. I believe that this is an exaggeration, since the discrepancy produces that kind of difference of a fraction of an oscillation.

34 Galileo, Dialogue on the Two Chief World Systems (1632), Edizione Nazionale , op. cit. (1), vii, 474–6, and Palmieri, op. cit. (1), 262–3.

35 Galileo, Edizione Nazionale , op. cit. (1), i, 323–8, is the most elaborate version of the battery of counterarguments levelled by Galileo at the theory of the punctum reflexionis in the whole of De motu .

36 The argument reconstructed by Galileo is rather obscure. Galileo's original Latin is as follows. ‘ Quod movetur ad aliquod punctum accedendo et ab eodem recedendo, ac ut fine et principio utendo, non recedet nisi in eo constiterit: at quod ad extremum lineae punctum movetur et ab eodem reflectitur, utitur eo ut fine et principio: inter accessum, ergo, et recessum ut stet, est necessarium ’. Galileo, Edizione Nazionale , op. cit. (1), i, 323–4.

37 Galileo, Edizione Nazionale , op. cit. (1), i, 326–8.

38 Experience does not teach causes, says Galileo: ‘ quaerimus enim effectuum causas, quae ab experientia non traduntur ’. Galileo, Edizione Nazionale , op. cit. (1), i, 263.

39 Galileo, Two New Sciences (1638), Edizione Nazionale , op. cit. (1), viii, 128–9, and Palmieri, op. cit. (1), 263–4.

40 Palmieri , P. , ‘ Galileo's construction of idealized fall in the void ’, History of Science ( 2005 ), 43 , 343 –89 CrossRef Google Scholar .

41 In order to get closer to the 1:100 ratio, I repeated the tests with a heavier lead ball, as shown in Video 26 (‘Cork lead 4lb interference’), and Videos 27 to 29 (‘cork lead 4lb discrepancy’). The lead ball was 1812 grams and the cork ball 18.5 grams, very close to the exact ratio claimed by Galileo. As Video 26 shows, the heavy lead ball causes some interference that somehow affects the results. The origin of this interference is mechanical, as will be explained below in this section. Unfortunately, the experiments with the heavy lead ball are affected by an interference that precludes further conclusions.

42 Palmieri, op. cit. (40); idem , ‘“… spuntar lo scoglio più duro”: did Galileo ever think the most beautiful thought experiment in the history of science?’, Studies in History and Philosophy of Science (2005), 36 , 223–40; and idem , ‘The cognitive development of Galileo's theory of buoyancy’, Archive for History of Exact Sciences (2005), 50 , 189–222.

43 Galileo, Edizione Nazionale , op. cit. (1), i, 273. Galileo is clear and honest. The proportions of motions calculated according to the Archimedean rules of the specific gravities do not pass the test of experience. Galileo does not say more about the tests.

44 An intriguing answer might be given by the tests made by Thomas Settle and Donald Miklich, even though the experiments only aimed at determining the plausibility of the empirical basis underlying another theory espoused by Galileo in De motu , namely the theory according to which light bodies fall faster than heavy bodies at the beginning of a free fall. See T. Settle, ‘Galileo and early experimentation’, in Springs of Scientific Creativity: Essays on Founders of Modern Science (ed. R. Aris, H. Ted Davis and Roger H. Stuewer), Minneapolis, 1983, 3–20.

45 See the ‘Supporting document’ for reasons why this arrangement is unconvincing.

46 ‘Pathway’ in the sense articulated by F. L. Holmes, Investigative Pathways: Patterns and Stages in the Careers of Experimental Scientists , New Haven and London, 2004.

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• Volume 42, Issue 4
• PAOLO PALMIERI (a1)
• DOI: https://doi.org/10.1017/S0007087409990033

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