The shape of a liquid surface in a rotating frame depends on the angular velocity. In this experiment, a fluid in a narrow rectangular container is placed on a rotating table. A smartphone fixed to the rotating frame records the fluid surface with its camera and, with a built-in gyroscope, the angular velocity. As the table rotates the surface evolves and develops a parabolic shape. Using video analysis we obtain the concavity of the parabola and the height of the vertex. Experimental results are compared with theoretical predictions. This problem contributes to improving the understanding of relevant concepts in fluid dynamics.

中文翻译：

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旋转坐标系中液体自由表面的实验分析

旋转坐标系中液面的形状取决于角速度。在这个实验中，一个狭窄的矩形容器中的流体被放置在一个旋转的桌子上。固定在旋转框架上的智能手机使用相机记录流体表面，并使用内置陀螺仪记录角速度。随着工作台旋转，表面演变并形成抛物线形状。使用视频分析，我们获得抛物线的凹度和顶点的高度。实验结果与理论预测进行了比较。这个问题有助于提高对流体动力学相关概念的理解。