Comptes Rendus
no. 5
Disk in a groove with friction: An analysis of static equilibrium and indeterminacy
Cesare Donolato1
1 Via dello Stadio 1A, 36100 Vicenza, Italy
Comptes Rendus. Mécanique, Volume 346 (2018) no. 5, pp. 384-389.

This note studies the statics of a rigid disk placed in a V-shaped groove with frictional walls and subjected to gravity and a torque. The two-dimensional equilibrium problem is formulated in terms of the angles that contact forces form with the normal to the walls. This approach leads to a single trigonometric equation in two variables whose domain is determined by Coulomb's law of friction. The properties of solutions (existence, uniqueness, or indeterminacy) as functions of groove angle, friction coefficient and applied torque are derived by a simple geometric representation. The results modify some of the conclusions by other authors on the same problem.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2018.03.001
Mots clés : Static friction, Disk equilibrium, Indeterminacy
Cesare Donolato 1

1 Via dello Stadio 1A, 36100 Vicenza, Italy 
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Cesare Donolato. Disk in a groove with friction: An analysis of static equilibrium and indeterminacy. Comptes Rendus. Mécanique, Volume 346 (2018) no. 5, pp. 384-389. doi : 10.1016/j.crme.2018.03.001. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2018.03.001/

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[4] W. Stamm Modellierung und Simulation von Mehrkörpersystemen mit flächigen Reibkontakten, Schriftenreihe des Instituts für Technische Mechanik, vol. 13, KIT Scientific Publishing, Karlsruhe, Germany, 2011

[5] L.E. Goodman; W.H. Warner Statics, Dover Publications, Mineola, New York, 2001

[6] C. Donolato The statics of the wedge-shaped jar-opener, Eur. J. Phys., Volume 36 (2015) (1–5)

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