On the ball on a string demonstration of angular momentum conservation

Abstract

The ‘ball on a string’ demonstration is a common tool used in physics education to illustrate the concept of conservation of angular momentum. However, various confounding factors can cause significant deviations from the idealized case, particularly under extreme conditions or when using low-stiffness pivots or high coefficients of friction. These factors include air resistance, contact friction at the pivot point, the mass of the ball and string, the angle of the string due to gravity, and the wobbling of the pivot point due to the centrifugal forces acting on it. In this work, we critically review by means of accurate simulations the adequateness of the ‘ball on a string’ demonstration in view of these confounding factors and provide recommendations for instructors on how to maximize the educational value of the demonstration while minimizing potential confusion for students. Our analysis suggests that a stiff pivot and avoiding extreme conditions are key to obtaining results that are in good agreement with the idealized case. We also caution instructors against using the demonstration without at least mentioning the confounding factors, as this may lead to a questionable understanding of the underlying physics principles.