Rocking Semicircular Hoop Model 1

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 in the American Journal of Physics.

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.