Slipping and rolling on an inclined plane

DOI10.1088/0143-0807/32/4/017zbMath1372.70019arXiv1106.2247OpenAlexW3101327096WikidataQ99713102 ScholiaQ99713102MaRDI QIDQ3087796

Amir Aghamohammadi, Cina Aghamohammadi

Publication date: 17 August 2011

Published in: European Journal of Physics (Search for Journal in Brave)

Abstract: In the first part of the article using a direct calculation two-dimensional motion of a particle sliding on an inclined plane is investigated for general values of friction coefficient ($mu$). A parametric equation for the trajectory of the particle is also obtained. In the second part of the article the motion of a sphere on the inclined plane is studied. It is shown that the evolution equation for the contact point of a sliding sphere is similar to that of a point particle sliding on an inclined plane whose friction coefficient is $$. If $mu>2/7anheta$, for any arbitrary initial velocity and angular velocity the sphere will roll on the inclined plane after some finite time. In other cases, it will slip on the inclined plane. In the case of rolling center of the sphere moves on a parabola. Finally the velocity and angular velocity of the sphere are exactly computed.

Full work available at URL: https://arxiv.org/abs/1106.2247

Mathematics Subject Classification ID

Problems involving a system of particles with friction (70F40) Motion of a rigid body in contact with a solid surface (70E18)

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