Collision of two balls in a groove -- An interplay between translation and rotation

TL;DR

This paper investigates the collision dynamics of two balls in a groove, analyzing how translation and rotation interplay to produce different trajectories, supported by theoretical derivations and experimental validation.

Contribution

It introduces a velocity diagram approach and a determinant criterion to distinguish trajectory types based on translation-rotation interplay after collisions.

Findings

Three distinct trajectory types depending on groove width

Velocity diagrams effectively predict trajectory outcomes

The determinant discriminates between different collision behaviors

Abstract

When two identical balls collide with equal inital speed on a horizontal groove, one can observe three trajectory types depending on the groove width. To explain this observation, we derive velocity diagrams of the balls motions from Newton's laws of translation and rotation and kinematics of rigid bodies in a three-dimensional vectorial representation and compare them with experimental results. The velocity diagrams and an introduced determinant allow to discriminate between the trajectory types and to understand the interplay between translation and rotation after the collision of the balls.