Galileo was the first to analyze the motion of spheres rolling down an inclined surface. Since then, Coulomb’s law of dry friction has covered the case of sliding particles. However, a particle that is not round can still roll, although in a way that is essentially different from the motion studied by Galileo. Instead of keeping contact with the surface, such particles will start bouncing after reaching a certain angular velocity. This motion is a combination of flying and colliding. It is shown that the acceleration of a bouncing particle is always bounded by the accelerations for perfect rolling and sliding. In order to describe the motion of a not perfectly round particle, the polygon is used as a model. The aim of the model is to predict the trajectories of particles that cannot be covered by the models for perfect rolling and sliding.

Issue Section:
Technical Papers
Keywords:
rotation, acceleration, rolling friction
Topics:
Collisions (Physics), Friction, Particulate matter, Rotation, Equations of motion
1.
Drake, S., 1978, Galileo at Work, His Scientific Biography, University of Chicago Press, Chicago, IL.
2.
Galileo, G., (ca., 1590 and ca. 1600), 1960, On Motion and on Mechanics, The University of Wisconsin Press, Translation by Drakbin and Drake.
3.
Shinohara
,
K.
,
1986
, “
Fundamental Analysis on Gravitational Separation of Differently Shaped Particles on Inclined Plates
,”
Powder Technol.
,
48
, pp.
151
–
159
.
4.
Azzoni
,
A.
,
La Barbera
,
G.
, and
Zaninetti
,
A.
,
1995
, “
Analysis and Prediction of Rockfall Using a Mathematical Model
,”
Int. J. Rock Mech. Min. Sci. Geomech. Abstr.
,
32
(
7
), pp.
709
–
724
.
5.
Hacar Benitez, M. A., Bollo, MI. F., and Hacar Rodrigues, M. P., 1977, “Bodies Falling Down on Different Slopes—Dynamic Study,” Proceedings of the 9th International Conference on Soil Mechanics and Foundation Engineering, MAA Publishing, pp. 91–95.
6.
Furuuchi
,
M.
, and
Gotoh
,
K.
,
1992
, “
Shape Separation of Particles
,”
Powder Technol.
,
73
, pp.
1
–
9
.
7.
Keller
,
J. B.
,
1986
, “
Impact With Friction
,”
ASME J. Appl. Mech.
,
53
, pp.
1
–
4
.
8.
Wang
,
Y.
, and
Mason
,
M. T.
,
1992
, “
Two-Dimensional Rigid-Body Collisions With Friction
,”
ASME J. Appl. Mech.
,
59
, pp.
635
–
642
.
9.
Petzold, L. R., 1982, “A Description of DASSL: Differential Algebraic System Solver,” SAND82-8637, Sandia National Laboratories, Sept.
10.
Brenan, K. E., Campbell, S. L., and Petzold, L. R., 1989, Numerical Solution of Initial Value Problems in Differential-Algebraic Equations, Elsevier, New York.
11.
Stoianovici
,
D.
, and
Hurmuzlu
,
Y.
,
1996
, “
A Critical Study of the Applicability of Rigid-Body Collision Theory
,”
ASME J. Appl. Mech.
,
63
, pp.
307
–
316
.
Copyright © 2003
 by ASME
You do not currently have access to this content.