9. Galileo's Discovery of the Law of Free Fall

The first attempted derivation by Galileo of the law relating space and time in free fall that has survived is preserved on an otherwise unidentified sheet bound among his manuscripts preserved at Florence. It is undoubtedly closely associated with a letter from Galileo to Paolo Sarpi, dated 16 October 1604, which somehow found its way into the Seminary of Pisa, where it is still preserved. Those two documents, together with the letter from Sarpi to Galileo which seems to have inspired them, are translated in full below. Sarpi's letter, dated 9 October 1604, suggests that recent oral discussions of problems of motion had recently taken place between the two men. It reads as follows:“In sending you the enclosure, it occurs to me to propose to you a problem to resolve, and another that seems to me paradoxical.

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Galileo and the Problem of Free Fall

The British Journal for the History of Science ◽

10.1017/s0007087400013108 ◽

1974 ◽

Vol 7 (2) ◽

pp. 105-134 ◽

Cited By ~ 23

Author(s):

R. H. Naylor

Keyword(s):

Precise Measurement ◽

Free Fall ◽

Present Knowledge ◽

Inclined Plane ◽

Clear View ◽

The Law ◽

Point Of Departure

There can be little doubt that 1973 will remain notable as a year in which knowledge of Galileo's mechanics increased dramatically. Professor Stillman Drake's publication, in May, of some of Galileo's early work on the law of free fall was followed in the autumn by the publication of a number of important manuscripts clearly indicating Galileo's use of precise measurement. From a discussion of these manuscripts and Thomas Settle's performance of Galileo's inclined plane experiment, Drake implies that a clear view of Galileo's use of experiment is now emerging. Added emphasis was given to Drake's thesis that doubts concerning Galileo's use of experiment were largely unfounded, by James MacLachlan's realization of a Galilean experiment which was previously described as ‘imaginary’ by Koyré. The purpose of this paper is to suggest that, while it cannot be doubted that Galileo used experiment and precise measurement, his attitude to observation may well have been far more complex than Drake has supposed. My point of departure is James MacLachlan's remark that continuing disagreement over Galileo's use of experiment should lead to further examination of Galileo's experimental claims. I shall indicate that more than one view of Galileo's use of experiment may prove capable of explaining our present knowledge—a corollary of this being that alternative explanations may be proposed for the manuscripts recently published by Drake.

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Physical Explication and Realization of the Turning Motion of a Cat by Analysis and Experiment Using a Robot Cat

Journal of Robotics and Mechatronics ◽

10.20965/jrm.1991.p0437 ◽

1991 ◽

Vol 3 (5) ◽

pp. 437-442

Author(s):

Takashi Kawamura ◽

◽

Kazuo Yamafuji ◽

Tsuyoshi Kobayashi

Keyword(s):

Computer Simulation ◽

Angular Momentum ◽

Dynamic Characteristics ◽

Free Fall ◽

Circular Column ◽

Turning Motion ◽

New Type ◽

The Law ◽

The One

Over turning motion of a cat at free fall in the air was investigated analytically and experimentally. Firstly, a live cat was modeled by a double circular column jointed with a spine at the one end of each column. And the dynamic characteristics of the model was analyzed based on the law of conservation of angular momentum. Then computer simulation was carried out. The results due to the simulation coincide well with those derived by the analysis, and validity of the modeling was shown. And a ROBOT CAT composed of a double circular column and a new type of backbone was developed in order to execute turning motion at free fall just like a cat. The robot successfully performed the complete overturning (180 degrees rotation) from the upside-down posture within 0.6 second. Therefore, the robot can change its posture to land on its feet if released from about 1.8m height quite upside-down.

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Galileo's Discovery of the Law of Free Fall

Scientific American ◽

10.1038/scientificamerican0573-84 ◽

1973 ◽

Vol 228 (5) ◽

pp. 84-92 ◽

Cited By ~ 23

Author(s):

Stillman Drake

Keyword(s):

Free Fall ◽

The Law

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The Geometrization of Motion: Galileo’s Triangle of Speed and its Various Transformations

Early Science and Medicine ◽

10.1163/157338210x516279 ◽

2010 ◽

Vol 15 (4-5) ◽

pp. 410-447 ◽

Cited By ~ 8

Author(s):

Carla Rita Palmerino

Keyword(s):

Free Fall ◽

Accelerated Motion ◽

The Law

This article analyzes Galileo’s mathematization of motion, focusing in particular on his use of geometrical diagrams. It argues that Galileo regarded his diagrams of acceleration not just as a complement to his mathematical demonstrations, but as a powerful heuristic tool. Galileo probably abandoned the wrong assumption of the proportionality between the degree of velocity and the space traversed in accelerated motion when he realized that it was impossible, on the basis of that hypothesis, to build a diagram of the law of fall. The article also shows how Galileo’s discussion of the paradoxes of infinity in the First Day of the Two New Sciences is meant to provide a visual solution to problems linked to the theory of acceleration presented in Day Three of the work. Finally, it explores the reasons why Cavalieri and Gassendi, although endorsing Galileo’s law of free fall, replaced Galileo’s diagrams of acceleration with alternative ones.

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Mental Imagery of Free Fall: Does a Falling Apple Accelerate in Our Minds?

Timing & Time Perception ◽

10.1163/22134468-bja10022 ◽

2021 ◽

pp. 1-11

Author(s):

Daniel Bratzke ◽

Rolf Ulrich

Keyword(s):

Mental Imagery ◽

Gravitational Force ◽

Time Estimation ◽

Free Fall ◽

Gravitational Acceleration ◽

Estimation Task ◽

Height Estimation ◽

Fall Time ◽

The Law ◽

Time Estimation Task

Abstract The present study examined whether people’s mental imagery of falling objects includes the acceleration due to the earth’s gravitational force. To investigate this question, we used two different tasks, a height estimation and a fall-time estimation task. In the height estimation task, participants were presented with different free-fall times and had to indicate the corresponding heights from which the object fell to the ground. In the fall-time estimation task, participants had to produce the fall time associated with free falls from different heights. In contrast to the law of free fall, our results are more consistent with a linear than with an accelerated relationship between height and fall time. Thus, the present results suggest that mental imagery of an object’s free fall does not represent the gravitational acceleration due to gravity.

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