A simple numerical model of the water bottle flipping experiment

The water bottle flip experiment is a recreational, non-conventional illustration of the conservation of angular moment. When a bottle partially filled with water is thrown in a rotational motion, water redistributes throughout the bottle, resulting in an increase of moment of inertia and thus to a decrease in angular velocity, which increases the probability of it falling upright on a table as compared with a bottle filled with ice. The investigation of this phenomenom is accessible to undergraduate students and should allow them to gain better understanding of combined translational and rotational motions in classical mechanics. In addition to reporting a series of detailed experiments and analyzing them using standard image analysis, we provide a simple theoretical framework and subsequent numerical implementation based on the decomposition of the water volume into thin slices of a rigid body that are subjected to fictitious forces in the non-inertial frame of the spinning bottle. This model allows us to capture quantitatively the main experimental findings, including the angular velocity slow-down for a given range of water filling fractions. Finally, we discuss additionnal counter-intuitive effects that contribute to bottle stabilization on landing.