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Free surface of a liquid in a rotating frame with time-depend velocity

The shape of liquid surface in a rotating frame depends on the angular velocity. In this experiment, a fluid in a rectangular container with a small width is placed on a rotating table. A smartphone fixed to the rotating frame simultaneously records the fluid surface with the camera and also, thanks to the built-in gyroscope, the angular velocity. When the table starts rotating the surface evolves and develops a parabolic shape. Using video analysis we obtain the surface's shape: concavity of the parabole and height of the vertex. Experimental results are compared with theoretical predictions. This problem contributes to improve the understanding of relevant concepts in fluid dynamics.