A Stable Cup of Coffee

Abstract
We investigate the optimal amount of liquid to place in a container, such as a soda can or cup of coffee, so that the angle at which the container will tip over is as large as possible.

Classic investigations assume that the water is static and does not flow as the can rotates (as would be the case with frozen water). We study the effect of allowing the water to flow. We develop an algorithm to solve the optimization problem for given can parameters (size and mass) and obtain various symbolic and geometric results.

The main open question is to prove several of the observed properties of the graph of the tipping angle as a function of the amount of water in the container.