A jumping cylinder on an inclined plane

  title={A jumping cylinder on an inclined plane},
  author={Roberto G'omez and J. J. Hern'andez-G'omez and Vivianne Marquina},
  journal={European Journal of Physics},
The problem of a cylinder of mass m and radius r, with its centre of mass out of the cylinder’s axis, rolling on an inclined plane that makes an angle α with respect to the horizontal, is analysed. The equation of motion is partially solved to obtain the site where the cylinder loses contact with the inclined plane (jumps). Several simplifications are made: the analysed system consists of an homogeneous disc with a one-dimensional straight line mass parallel to the disc axis at a distance y < r… 

Figures and Tables from this paper

Modeling and experimentation with asymmetric rigid bodies: a variation on disks and inclines
We study the ascending motion of a disk rolling on an incline when its centre of mass lies outside the disk axis. The problem is suitable as laboratory project for a first course in mechanics at the
Librational motion of asymmetric rolling bodies and the role of friction force
We designed a very simple asymmetric rolling spool and we studied it experimentally, in the librational regime, by using a video camera and video analysis software. Comparison of experimental results
The surprising rolling spool: librational motion and failure of the pure rolling condition
In a previous work (Onorato P, Malgieri M, Mascheretti P and De Ambrosis A 2014 The surprising rolling spool: experiments and theory from mechanics to phase transitions Eur. J. Phys. 35 055011) an
The surprising rolling spool: experiments and theory from mechanics to phase transitions
An asymmetric rolling spool can be investigated as a simple model for a second-order phase transition. At low energy it undergoes librational motion around the equilibrium position, whereas at high
Ascending Disk: Theoretical and Numerical Study
This work analyzed a classical mechanical problem: a disc with a circular hole rotating and ascending on a inclined plane to show the basic equations in both Lagrangian and Newtonian formalisms and to present numerical solutions.
The eccentric disk and its eccentric behavior
Providing example problems that stimulate curiosity and cultivate intuition among students is a prominent responsibility for physics educators. A concept that can be particularly challenging for
Tautochrone and Brachistochrone Shape Solutions for Rocking Rigid Bodies
Rocking rigid bodies appear in several shapes in everyday life: As furniture like rocking chairs and rocking cradles or as toys like rocking horses or tilting dolls. The familiar rocking motion of
Use of Dimensional Analysis in the X-, Y-, and Z-Axis to Predict Occurrence of Injury in Human Stampede
Real-time video-analysis monitoring of high capacity events or those with known nozzle effects for loss of proxemics and Z-axis displacement pathology offers the opportunity to prevent mortality from human stampedes.


Dissipative descent: rocking and rolling down an incline
We consider the dynamics of a hollow cylindrical shell that is filled with viscous fluid and another, nested solid cylinder, and allowed to roll down an inclined plane. A mathematical model is
Rules for rolling as a rotation about the instantaneous point of contact
It is a widespread misunderstanding in introductory physics courses that the motion of rolling bodies in general can be calculated using the point of contact as a reference point when equating the
Rolling of asymmetric disks on an inclined plane
In a recent papers, Turner and Turner (2010 {\em Am. J. Phys.} {\bf 78} 905-7) and Jensen (2011 {\em Eur. J. Phys.} {\bf 32} 389-397) analysed the motion of asymmetric rolling rigid bodies on a
Asymmetric rolling bodies and the phantom torque
The center of mass and the point of contact of two-dimensional rolling bodies are used almost interchangeably to understand the dynamics of rolling bodies in introductory physics courses. The use of
Experiments and computer simulations show that when a rigid ball with inhomogeneous but symmetric density distribution rolls on an inclined track, it tends to adjust its orientation to rotate about
Rolling motion of non-axisymmetric cylinders
Theoretical and experimental results are compared for the rolling motion of cylinders on a ramp. An asymmetric distribution of the mass makes the motion jerky and complex and is an interesting and
Study of equations for Tippe Top and related rigid bodies
The Tippe Top consist of a small truncated sphere with a peg as a handle. When it is spun fast enough on its spherical part it starts to turn upside down and ends up spinning on the peg. This count
Dynamics of Multibody Systems
This paper presents a meta-modelling procedure that automates the very labor-intensive and therefore time-heavy and therefore expensive and expensive process of designing and implementing Rigid Body Kinematics Systems.
Mechanics (Course of Theoretical Physics vol 1) 3rd edn (Oxford: Pergamon
  • 1976