written by Wolfgang Christian

The Rocking Semicircular Hoop model shows the dynamics of a simple object rocking without slipping on a horizontal surface.  It is a supplemental simulation for an article by Leaf Turner and Ari Turner  "Asymmetric rolling bodies and the phantom torque" in the Am. J. Phys. 78, 905 (2010).

The object, a semicircular hoop with radius R, is acted on by gravitational, frictional, and normal forces.   Although the system executes simple harmonic motion at small angles, its large angle oscillations are nonlinear.  The angular acceleration for the semicircular hoop can be derived through Lagrangian dynamics or by computing the torque about the point of contact.  The paper by Turner and Turner derives the equation of motion from an analysis of the torque and the Rocking Semicircular Hoop model displays the numerical solution and shows how the forces and torques evolve in time.

The Rocking Semicircular Hoop model was created using the Easy Java Simulations (EJS) modeling tool.  It is distributed as a ready-to-run (compiled) Java archive.  Double clicking the ejs_mech_lagrangian_RockingSemicircularHoop.jar file will run the program if Java is installed.

• Download ejs_mech_lagrangian_RockingSemicircularHoop.jar - 1236kb Java Archive File

Last Modified June 12, 2014

This file has previous versions.

The source code zip archive contains an XML representation of the Rocking Semicircular Hoop model.   Unzip this archive in your EJS workspace to compile and run this model using EJS.

• Download ejs_mech_lagrangian_RockingSemicircularHoop.zip - 33kb Compressed File

Last Modified August 14, 2010

This file has previous versions.