A series of experiments for steady state rotation of water in vessels of various geometries is presented. The experiments focus on the geometrical characteristics of the rotating liquids and the change in their surface topology, from that akin to a sphere to that of a torus (i.e., from genus 0 to 1), for sufficiently large angular speeds. Cylindrical, planar rectangular, cubic, spherical, and conical containers are considered. The cone is an exception as some liquid always remains in its apex, no matter how fast the spin. It is shown also that for any amount of liquid within, there exists a critical angular speed above which the liquid can no longer be confined and is therefore expelled from the cone spontaneously breaking the symmetry. This instability is investigated experimentally.

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See supplemental material for a video showing the development of the instability and spill in the cone for the initial fill level h = 3 cm, filmed from above as shown in Fig. 2.

Supplementary Material

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