Modern mobile phones contain a three-axis microelectromechanical system (MEMS) gyroscope, capable of taking accurate measurements of the angular velocity along the three principal axes of the phone with a sampling rate of 100 Hz or better. If the phone is tossed in the air, then, neglecting air resistance, it is in free rotation (rotation in the absence of a torque) with respect to its centre of mass, and the phone's gyroscope can be used to record the rotational dynamics. This enables experimental investigation of free rotation. In this paper, we use a mobile phone to demonstrate the steady states for rotation of the phone about two of its principal axes, and the instability in rotation about the third corresponding to the intermediate moment of inertia. We also show the approximate conservation of angular momentum and rotational kinetic energy during motion in the air, and compare the data with numerical solution of Euler's equations for free rotation. Our results demonstrate the capability of smartphones for investigating free rotation, and should be of interest to college and university teachers developing “at home” physics labs for remote learning.

中文翻译：

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手机作为自由旋转的实验室

现代手机包含三轴微机电系统（MEMS）陀螺仪，能够以100 Hz或更高的采样率精确测量沿手机三个主轴的角速度。如果将手机抛向空中，则可以忽略空气阻力，使其相对于质心自由旋转（在没有扭矩的情况下旋转），并且可以使用手机的陀螺仪记录旋转动态。这使得能够进行自由旋转的实验研究。在本文中，我们使用移动电话演示了电话围绕其两个主轴旋转的稳态，以及与中间惯性矩相对应的围绕第三个轴线旋转的不稳定性。我们还展示了在空气中运动期间角动量和旋转动能的近似守恒，并将数据与自由旋转的欧拉方程的数值解进行了比较。我们的研究结果证明了智能手机具有研究自由旋转的功能，并且对于开发用于远程学习的“在家”物理实验室的大学和大学教师应该引起人们的兴趣。