Inelastic Collisions of Two Rough Spheres

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

This Demonstration models inelastic collisions between two rough hard spheres of equal uniform density. You can vary the coefficient of normal restitution , the coefficient of tangential restitution , the relative mass , the impact parameter , and the initial angular velocity of the sphere moving from the left (the sphere rotates about an axis perpendicular to the collision plane). The coefficient of normal restitution ranges from (a perfectly inelastic collision) to (a perfectly elastic collision), while the coefficient of tangential restitution ranges from (in which the spheres are perfectly smooth) to (in which the spheres are perfectly rough). The total kinetic energy is conserved only if and either or . You can observe the collision in slow motion in either the laboratory or the center-of-mass frame of reference. The spheres leave dotted contrails to help you trace their trajectories.


In order to get more quantitative informations out of the settings of the different parameters, a goniometer was added, which can be positioned to the centers of either particle in the instant of the impact. The different positions are especially useful in the center of mass-system. The trajectories of the particles are now dashed to visualize the velocities.


Contributed by: Andrés Santos (February 2010)
Changes by: Hans-Joachim Domke
Open content licensed under CC BY-NC-SA




Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.