BS in Physics
At some point while consuming a beverage, many people will idly try to balance its container on edge. The act itself is physically straightforward, merely involving the system's center of mass and achieving a static equilibrium between the opposing torques caused by gravity and the normal force between the container and the surface on which it balances. Further analysis of the act, however, illuminates the richness of the exercise.
These nuances are apparent even in simplified two-dimensional models because of the depth of the relationship between a container's geometry and achieving balance. The purpose of such analysis is threefold: first, when considering a rectangular container, to determine the relationship between the angle at which it balances and the amount of fluid in the container; second, to consider a massless analogue to a standard twelve-ounce aluminum can which balances at a fixed angle and observe the interplay between the various parameters of that container's geometry and balance; and finally, to revisit the aluminum can model, this time considering its mass relative to the fluid's, and recover the familiar behavior observed when balancing real-world beverages in aluminum cans.