# A jumping cylinder on an inclined plane

@article{Gomez2012AJC, 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}, year={2012}, volume={33}, pages={1359-1365} }

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…

## 8 Citations

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## References

SHOWING 1-10 OF 12 REFERENCES

Control of motion of an inhomogeneous cylinder with internal movable masses along a horizontal plane

- Engineering
- 2006

Dissipative descent: rocking and rolling down an incline

- EngineeringJournal of Fluid Mechanics
- 2007

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

- Physics
- 2011

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

- Physics
- 2011

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

- Physics
- 2010

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…

ROLLING DYNAMICS OF AN INHOMOGENEOUS BALL ON AN INCLINED TRACK

- Physics
- 2008

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

- Physics, Engineering
- 2005

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

- Physics
- 2010

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

- Engineering
- 2007

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.

Dynamics of Multibody Systems (Berlin: Springer) problem

- 2008