The toppling motion of a uniform rectangular block is investigated as a function of the friction between its pivot edge and the horizontal surface on which it rests. Initially, the edge of the block remains stationary, but it inevitably slips before the block lands. The inclination angle at which slipping occurs and the direction of slip depend on the coefficient of static friction. The toppling motion of a granite block was monitored at 400 Hz with MEMs gyro/accelerometers at the center of mass and at the pivot edge, as well as by “Tracker” analysis of video recorded at 240 fps.
REFERENCES
1.
Tad
McGeer
and
Leigh Hunt
Palmer
, “
Wobbling, toppling, and forces of contact
,” Am. J. Phys.
57
, 1089
–1098
(1989
).2.
Leaf
Turner
and
Jane l.
Pratt
, “
Does a falling pencil levitate
?,” Quantum
8
(4
), 22
–25
(1998
), https://static.nsta.org/pdfs/QuantumV8N4.pdf.3.
Rod
Cross
, “
The fall and bounce of pencils and other elongated objects
,” Am. J. Phys.
74
(1
), 26
–30
(2006
).4.
Vitor
Oliveira
, “
Experiments with a falling rod
,” Am. J. Phys.
84
, 113
–117
(2016
).5.
Stephen T.
Thornton
and
Jerry B.
Marion
, Classical Dynamics of Particles and Systems
(
Thompson Brooks Cole
, Belmont, CA
, 2004
).6.
Peter F.
Hinrichsen
, “
Fourier analysis of the non-linear pendulum
,” Am. J. Phys.
88
(12
), 1068
–1075
(2020
).7.
Zhao
Zhen
,
Caishan
Liu
, and
Nannan
Wang
, “
Rocking dynamics of a planar rectangular block on a rigid surface
,” Multibody Syst. Dyn.
45
(3
), 105–125
(2019
).8.
Hongjian
Zhang
,
Bernard
Brogliato
, and
Caishan
Liu
, “
Dynamics of planar rocking-blocks with Coulomb friction and unilateral constraints: Comparisons between experimental and numerical data
,” Multibody Syst. Dyn.
32
(1
), 1
–25
(2014
).9.
Shiliang
Shan
,
Jennifer A.
Shore
, and
Kristine
Spekkens
, “
The falling rod race
,” Phys. Teach.
58
, 596
–598
(2020
).10.
11.
W. M.
Young
, “
Faster than gravity
,” Am. J. Phys.
52
(12
), 1142
–1143
(1984
).12.
W. F. D.
Theron
, “
The ‘faster than gravity’ demonstration revisited
,” Am. J. Phys.
56
, 736
–739
(1988
).13.
Francis P.
Bundy
, “
Stresses in freely falling chimneys and columns
,” J. Appl. Phys.
11
, 112
–123
(1940
).14.
Gabriele
Varieschi
and
Kaoru
Kamiya
, “
Toy models for the falling chimney
,” Am. J. Phys.
71
(10
), 1025
–1031
(2003
).15.
Peter F.
Hinrichsen
, “
The physics of falling chimney stacks
,” Phys. Educ.
56
(5
), 055023
(2021
).16.
A.
Kaps
and
F.
Stallmach
, “
Tilting motion and the moment of inertia of the smartphone
,” Phys. Teach
58
(3
), 216
–217
(2020
).17.
Peter F.
Hinrichsen
, “
Compound pendulum pivot force
,” Eur. J. Phys.
42
(2
), 025001
(2020
).18.
Eugene I.
Butikov
, “
Oscillations of a simple pendulum with extremely large amplitudes
,” Eur. J. Phys.
33
(6
), 1555
–1563
(2012
).19.
Andrea
Bel
,
W.
Reartes
, and
A.
Torresi
, “
Global study of the simple pendulum by the homotopy analysis method
,” Eur. J. Phys.
33
(2
), 231
–238
(2012
).20.
See <https://mbientlab.com/> for “
MbientLab Inc.,
Metamotion MMR Wearable Bluetooth 9-Axis IMU
” (2018
).21.
22.
See
Douglas
Brown
, <https://physlets.org/tracker/> for “
Tracker Video Analysis and Modelling Tool (Version 5.1.5)
” (2009
).23.
Martin
Lieberherr
, “
Figuring the acceleration of the simple pendulum
,” Phys. Teach.
49
(9
), 576
–577
(2011
).24.
Carl E.
Mungan
and
Trevor C.
Lipscombe
, “
Oscillations of a quadratically damped pendulum
,” Eur. J. Phys.
34
, 1243
–1253
(2013
).25.
Peter F.
Hinrichsen
, “
Angular acceleration of the non-linear pendulum
,” Phys. Educ.
55
, 055018
(2020
).26.
Amin
Rezaeezadeh
, “
Motion of a hexagonal pencil on an inclined plane
,” Am. J. Phys.
77
, 401
–406
(2009
).27.
Rod
Cross
, “
The fall of an inclined rod
,” Eur. J. Phys.
42
, 055005
(2021
).28.
Pasco Scientific
, PASPORT Force Platform PS-2141
(
Pasco Scientific
, Roseville, CA
, 2020
).29.
Peter F.
Hinrichsen
, The Dynamics of Toppling Rectangular Blocks
(
Researchgate
, Berlin
, 2021
).30.
See supplementary material at https://www.scitation.org/doi/suppl/10.1119/10.0005889 for videos showing different toppling conditions.
© 2021 Author(s). Published under an exclusive license by American Association of Physics Teachers.
2021
Author(s)
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.
