Lawn tennis balls, Rolling friction experiment and Trouton viscosity

TL;DR

This study measures the rolling friction coefficients of tennis balls with different ages and estimates the core's viscosity using theoretical models, finding consistent results between experiments and theory.

Contribution

It introduces a method to relate rolling friction coefficients of tennis balls to the viscosity of their rubber cores using Trouton ratio assumptions.

Findings

Rolling friction coefficients are proportional to angular velocity.

Experimental and theoretical estimates of core viscosity are of similar magnitude.

Older and newer tennis balls show measurable differences in friction coefficients.

Abstract

We took three lawn tennis balls arbitrarily. One was moderately old, one was old and another was new. Fabricating a conveyor belt set-up we have measured rolling friction coefficients, $\mu_{r}$, of the three balls as a function of their angular velocities, $\omega_{ball}$. In all the three cases, plotting the results and using linear fits, we have obtained relations of the form $\mu_{r}= k_{rol} \omega_{ball}$ and have deduced the proportionality constant $k_{rol}$. Moreover, core of a lawn tennis ball is made of vulcanised India-rubber. Using the known values of Young modulus and shear viscosity of vulcanised India-rubbers in the theoretical formula for $k_{rol}$, we estimate $k_{rol}$s for the cores made of vulcanised India-rubbers, assuming Trouton ratio as three. The experimental results for the balls and the semi-theoretical estimates for the cores, of $k_{rol}$, are of the same order of magnitudes.