A washer on a vertical steel rod may start spinning instead of simply sliding down. The forces on the washer are analyzed, and the relationship between the angular velocity of rotation and the angular velocity of precession is obtained. A relationship about the coefficient of friction of the washer is obtained at the condition of rotation without slipping. The influence of the coefficient of friction and the ratio of the inner diameter of the washer to the diameter of the rod on the sliding state was investigated experimentally, and a two-dimensional phase diagram of the rotation without slipping was obtained. The relationship between the three parameters(the nutation angle of the washer, the angular velocity of precession, and the final vertical velocity) and the ratio of the inner diameter of the washer to the diameter of the rod in the condition of rotation without slipping was further investigated. The experimental results are in good agreement with the theoretical equations.

中文翻译：

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垫圈在垂直钢棒上的运动


垂直钢杆上的垫圈可能会开始旋转，而不是简单地向下滑动。分析了垫圈上的受力，得到了旋转角速度与进动角速度之间的关系。得到了在无滑动旋转情况下垫圈摩擦系数的关系。实验研究了摩擦系数以及垫圈内径与杆径之比对滑动状态的影响，得到了无滑移旋转的二维相图。旋转无滑移情况下，三个参数（垫圈章动角、进动角速度、最终垂直速度）与垫圈内径与杆直径之比的关系为进一步调查。实验结果与理论方程吻合良好。