In his Discorsi, Galileo aimed to correct centuries of Aristotelian “unreason” concerning the physics of falling objects by introducing a thought experiment that pointed out contradictions when combinations of one light and one heavy body are dropped. Inspired by Galileo's story, we sought to formulate research questions and design experiments for students to enable independent learning based on the history of science. The experiments involve commonly used or inexpensive equipment and free software, and show that Aristotle and Galileo did not disagree about falling objects, but were focusing on different kinds of motion. We assess data generated by high-speed video motion tracking of the fall of various combinations of simple handmade paper cones, following closely the discussion between Simplicio, Salviati and Sagredo in the Discorsi, and demonstrate that every statement in Galileo's reductio ad absurdum holds true and that his argument is in fact free of contradiction.

1.
Barry M.
Casper
, “
Galileo and the fall of Aristotle: A case of historical injustice?
,”
Am. J. Phys.
45
(
4
),
325
330
(
1977
).
2.
Galileo
Galilei
,
Dialogues Concerning Two New Sciences
, translated from the Italian and Latin into English by Henry Crew and Alfonso de Salvio (
Macmillan
,
New York
,
1914
), pp.
63
64
.
3.
Lythcott pointed out in an article that the term “Aristotelian” no longer means “following Aristotle” [
Jean
Lythcott
, “
Aristotelian was given as the answer, but what was the question?
,”
Am. J. Phys.
53
(
5
),
428
432
(
1985
)]. Rather, it has become a catchy and widely accepted label for the common-sense belief system about motion in contrast to the formal Newtonian system. This does Aristotle and his achievements a major disservice. Therefore, we will use the term in its original meaning and mark it if we do otherwise.
4.
Douglas
Brown
and
Anne J.
Cox
, “
Innovative uses of video analysis
,”
Phys. Teach.
47
(
3
),
145
150
(
2009
).
5.
P.
Klein
,
S.
Gröber
,
J.
Kuhn
, and
A.
Müller
, “
Video analysis of projectile motion using tablet computers as experimental tools
,”
Phys. Educ.
49(1)
,
37
40
(
2014
).
6.
Priscilla
Laws
and
Hans
Pfister
, “
Using digital video analysis in introductory mechanics projects
,”
Phys. Teach.
36
(
5
),
282
287
(
1998
).
7.
V.
Timková
and
Z.
Ješková
, “
How magnus bends the flying ball–experimenting and modeling
,”
Phys. Teach.
55
(
2
),
112
114
(
2017
).
8.
Ralf
Widenhorn
, “
The physics of juggling a spinning ping-pong ball
,”
Am. J. Phys.
84
(
12
),
936
942
(
2016
).
9.
Ann-Marie
Pendrill
,
Peter
Ekström
,
Lena
Hansson
,
Patrik
Mars
,
Lassana
Ouattara
, and
Ulrika
Ryan
, “
The equivalence principle comes to school–falling objects and other middle school investigations
,”
Phys. Educ.
49
(
4
),
425
430
(
2014
).
10.
Norman F.
Derby
,
Robert G.
Fuller
, and
Phil W.
Gronseth
, “
The ubiquitous coffee filter
,”
Phys. Teach.
35
(
3
),
168
171
(
1997
).
11.
The HTL Traun (HTL stands for “Höhere Technische Lehranstalt”) is a “higher vocational-technical school” specialized in IT security can be determined at <http://www.htltraun.at> (accessed August 18,
2018
).
12.
See supplementary material at https://doi.org/10.1119/1.5062167 for high-speed video of dropping three stacked cones compared to two stacked cones and a single cone conjoined by thread.
13.
More information on the JVC GC-PX10 can be determined at <http://de.jvc.com/microsite/de/gc-px10/index.html> (accessed April 15,
2017
).
14.
More information on the Tracker can be determined at <http://physlets.org/tracker/> (accessed August 18,
2018
).
15.
Yan
Feng
,
John
Goree
, and
Bin
Liu
, “
Accurate particle position measurement from images
,”
Rev. Sci. Instrum.
78
(
5
),
053704
(
2007
).
16.
Yan
Feng
,
John
Goree
, and
Bin
Liu
, “
Errors in particle tracking velocimetry with high-speed cameras
,”
Rev. Sci. Instrum.
82
(
5
),
053707
(
2011
).
17.
Pirooz
Mohazzabi
, “
When does air resistance become significant in free fall?
,”
Phys. Teach.
49(2)
,
89
90
(
2011
).
18.
We think a more detailed discussion would go beyond the scope of this paper, but we would like to refer to some work we found inspiring. [See
Shouryya
Ray
and
Jochen
Fröhlich
, “
An analytic solution to the equations of the motion of a point mass with quadratic resistance and generalizations
,”
Arch. Appl. Mech.
85
(
4
),
395
414
(
2015
), or for instance,
Peter
Timmerman
and
Jacobus P.
van der Weele
, “
On the rise and fall of a ball with linear or quadratic drag
,”
Am. J. Phys.
67
(
6
),
538
546
(
1999
).]
19.
John K.
Wood
, “
Aristotle and the physics student
,”
Am. J. Phys.
26
(
3
),
175
178
(
1958
).
20.
Hans-Joachim
Schlichting
, “
Wie frei ist der freie Fall?
,” in
Chemiedidaktik im Wandel – Gedanken zu einem neuen Chemieunterricht
edited by
E.
Sumfleth
(
Lit-Verlag, Münster
,
1999
), pp.
255
277
.
21.
Carl G.
Adler
and
Byron L.
Coulter
, “
Aristotle: Villain or Victim?
,”
Phys. Teach.
13
(
1
),
35
37
(
1975
).
22.
Edward M.
Purcell
, “
Life at low Reynolds number
,”
Am. J. Phys.
45
(
3
),
3
11
(
1977
).
23.
Lukas
Schwarz
,
Mariana
Medina-Sánchez
, and
Oliver G.
Schmidt
, “
Hybrid biomicromotors
,”
Appl. Phys. Rev.
4
(
3
),
031301
(
2017
).
24.
Martin
Kaltenbrunner
 et al, “
An ultra-lightweight design for imperceptible plastic electronics
,”
Nature
499
(
7459
),
458
463
(
2013
).
25.
Video of an ultra-lightweight electronic foil dropped in air
,” <https://media.nature.com/original/nature-assets/nature/journal/v499/n7459/extref/nature12314-sv1.mov> (accessed August 18,
2018
).
26.
GoPro: Red Bull Stratos–The Full Story
,” <https://www.youtube.com/watch?v=dYw4meRWGd4> (accessed August 18,
2018
).
27.
Markus
Guerster
and
Ulrich
Walter
, “
Aerodynamics of a highly irregular body at transonic speeds—Analysis of STRATOS flight data
,”
PLoS One
12
(
12
),
e0187798
(
2017
).

Supplementary Material

AAPT members receive access to the American Journal of Physics and The Physics Teacher as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.