圆圈的回滚运动分析及运动时间研究-常州工学院学报

文章信息/Info

Title:: Analysis of the Circular Loop′s Rollback and Its Motion Time′s Research

摘要:: 针对体育运动中圈的回滚问题，建立力学模型并求解。圆圈运动可分为带滑前滚、带滑后滚和无滑动滚动三个阶段。为保证回滚，圆圈的角速度必须按原来的方向转动，圈所受摩擦力方向由地面接触点的速度方向确定。圈的运动为合成运动，由质心运动定理列出加速度和角加速度的方程，积分后得到三阶段中角速度、质心速度、与地面接触点的速度和滚动路程随时间的变化规律。另外，给出总回滚时间表达式，并求出其极小值。最后将结论推广到其他圆形均质物体。

Abstract:: For the circular loop′s rollback problems,there are three stages in the loop′s motion: for-ward roll with sliding,backward roll with sliding and roll without sliding.To roll back,the rotating direction of angular velocity must be the same as the original direction.The friction′s direction is decided upon the ve-locity direction of the contact point with the ground.The loop′s motion is a resultant motion,and the equa-tions of the acceleration and the angular acceleration is listed according to the mass center′s kinematical mo-tion theorem.After integration,the law that the angular velocity,the mass center′s velocity and the ground contacting point′s velocity vary with time is obtained.Furthermore, the expression of the overall rollback time is yielded and its minimum value is given.Finally the conclusions are extended to other homogeneous circular object.