Analysis of the Changes in Velocity of Balls Rolling off Edges using Chi-squared Model Testing

Abstract

When a ball rolls over the edge of a table, its horizontal velocity is consistently observed to be higher than the initial horizontal velocity. While multiple studies have investigated this phenomenon, none of these studies provided data on the linear velocity of the ball, nor discussed the variance between the data and the model. This paper studied the motion of a ball rolling over the edge using chi-squared curve fitting and model testing. Video analysis was used to collect velocity data of the ball’s motion, and chi-square curve fitting and analysis was performed using a python script. The kick in velocity was observed to decrease as the initial velocity increased, consistent with previous studies. However, the best fit parameter values were not consistent with the derived theoretical model. Furthermore, chi-squared analysis indicated that the best fit model was not a good fit for the data, suggesting that revisions are necessary to the experiment and model.