The motion of a washer on a vertical steel rod

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.