In this paper we review the theory of the “falling chimney,” which deals with the breaking in mid-air of tall structures when they fall to the ground. We show that these ruptures can be caused by either shear forces typically developing near the base, or by the bending of the structure which is caused primarily by the internal bending moment. In the latter case the breaking is more likely to occur between one-third and one-half of the height of the chimney. Small scale toy models are used to reproduce the dynamics of the falling chimney. By examining photos taken during the fall of these models we test the adequacy of the theory. This type of experiment, which is easy to perform and conceptually challenging, can become part of a rotational mechanics lab for undergraduate students.

1.
R. M. Sutton, Demonstration Experiments in Physics (McGraw–Hill, New York, 1938).
2.
W. A. Hilton, Physics Demonstration Experiments at William Jewell College (William Jewell College, Liberty, 1971).
3.
G. D. Freier and F. J. Anderson, A Demonstration Handbook for Physics (American Association of Physics Teachers, College Park, 1981).
4.
D. R. Carpenter and R. B. Minnix, The Dick and Rae Physics Demo Notebook (Dick and Rae, Lexington, 1993).
5.
K. Kamiya and G. Varieschi, The Falling Chimney Web Page (http://myweb.lmu.edu/gvarieschi/chimney/chimney.html).
6.
P. A.
Constantinides
, “
Experiments on torque, angular acceleration and moment of inertia
,”
Am. J. Phys.
7
,
254
257
(
1939
).
7.
C. A.
Ludeke
, “
Experimental examples in dynamics
,”
Am. J. Phys.
9
,
162
166
(
1941
).
8.
W. A.
Hilton
, “
Free fall paradox
,”
Phys. Teach.
3
,
323
324
(
1965
).
9.
W. M.
Young
, “
Faster than gravity!
,”
Am. J. Phys.
52
,
1142
1143
(
1984
).
10.
F. M.
Phelps
and
L. R.
Clifford
, “
How the ant got into the dish
,”
Phys. Teach.
1
,
293
294
(
1986
).
11.
W. F.
Theron
, “
The faster than gravity demonstration revisited
,”
Am. J. Phys.
56
,
736
739
(
1988
).
12.
H.
Hartel
, “
The falling stick with a greater than g,
Phys. Teach.
38
,
54
55
(
2000
).
13.
L. A. Bloomfield, How Things Work (Wiley, New York, 1997).
14.
R. M.
Sutton
, “
Some teasers for conclusion jumpers
,”
Am. J. Phys.
21
,
658
(
1953
).
15.
J. S.
Miller
, “
On demonstrating a classical problem in analytical mechanics
,”
Am. J. Phys.
20
,
455
456
(
1952
).
16.
G. W.
Ficken
, “
Falling faster than g,
Am. J. Phys.
41
,
1013
1015
(
1973
).
17.
A. A.
Bartlett
, “
Falling chimney apparatus modification
,”
Phys. Teach.
13
,
435
437
(
1975
).
18.
J. L.
Adams
, “
Acceleration greater than g,
Phys. Teach.
20
,
100
101
(
1982
).
19.
U.
Haber-Schaim
, “
On qualitative problems
,”
Phys. Teach.
30
,
260
(
1992
).
20.
F. P.
Bundy
, “
Stresses in freely falling chimneys and columns
,”
J. Appl. Phys.
11
,
112
123
(
1940
).
21.
A. A.
Bartlett
, “
More on the falling chimney
,”
Phys. Teach.
14
,
351
353
(
1976
).
22.
R. M.
Sutton
, “
Concerning falling chimneys
,”
Science (Washington, DC, U.S.)
84
,
246
247
(
1936
).
23.
J. B.
Reynolds
, “
Falling chimneys
,”
Science (Washington, DC, U.S.)
87
,
186
188
(
1938
).
24.
E. L.
Madsen
, “
Theory of the chimney breaking while falling
,”
Am. J. Phys.
45
,
182
184
(
1977
).
25.
A. T.
Jones
, “
The falling chimney
,”
Am. J. Phys.
14
,
275
(
1946
).
26.
J. Walker, The Flying Circus of Physics with Answers (Wiley, New York, 1975).
27.
S. B. Cahn and B. E. Nadgorny, A Guide to Physics Problems—part 1 (Plenum, New York, 1994).
28.
J. A. Cronin and V. L. Telegdi, Graduate Problems in Physics (University of Chicago Press, Chicago, 1979).
29.
This is in general a good approximation. For a right circular hollow cylinder of outer and inner radii r1,r2 and length H, hinged at one end, the moment of inertia is I=m((r12+r22)/4+13H2)≃13mH2 for r1,r2≪H. For a typical chimney r1≲H/10, thus (r12/4)/(H2/3)≲0.0075, i.e., a correction of less than 1%. The correction due to r2 is even smaller.
30.
R. C. Hibbeler, Structural Analysis (Prentice–Hall, Upper Saddle River, NJ, 2002).
31.
R. C. Hibbeler, Mechanics of Materials (Prentice–Hall, Upper Saddle River, NJ, 1997).
32.
The bending moment and the stress forces can be thought as applied to the center (centroid) of the cross-sectional area we are considering, on the face belonging to the lower portion of the structure. Equal and opposite forces and moments would originate on the face belonging to the upper portion.
33.
A positive sign in the relation between bending moment and shear is usually reported in textbooks on statics, due to a different choice of the sign of the moment.
34.
A. Sommerfeld, Mechanics of Deformable Bodies (Academic, New York, 1950).
35.
L. D. Landau and E. M. Lifshitz, Theory of Elasticity (Pergamon, New York, 1986).
36.
G. Varieschi (unpublished).
37.
We did not find any use of toy models for this problem, either in the literature or in web-pages devoted to physics demos. We will be grateful to receive information about similar experiments, if any.
38.
G. Tonzig, Cento Errori di Fisica (Sansoni, Bologna, Italy, 1991).
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