论文标题
粒子在摩擦力的存在下在转盘上滑动
Particle sliding on a turntable in the presence of frictional forces
论文作者
论文摘要
研究了点粒子在转盘上滑动的运动。假设表将摩擦力施加在粒子上，该方程是在恒定幅度上施加摩擦力的，该方程与粒子相对相对于转门的运动方向相反。用无量纲变量表示方程后，讨论了解决方案的某些一般属性。在（i）相对于实验室框架中释放粒子的情况以及（ii）粒子相对于转盘释放粒子。然后对方程进行数值求解，以使对运动有更完整的了解。发现人们可以为粒子定义逃生速度，这是使粒子移至无穷大所需的最低速度。逃逸速度是距转盘中心的距离的函数，并且在距中心距离的距离方面，这取决于初始速度的方向。对这种行为的定性解释是用虚拟力量给出的。数值研究还表明了测量粒子和转盘之间摩擦系数的另一种方法。
Motion of a point particle sliding on a turntable is studied. The equations of motion are derived assuming that the table exerts frictional force on the particle, which is of constant magnitude and directed opposite to the direction of motion of the particle relative to the turntable. After expressing the equations in terms of dimensionless variables, some of the general properties of the solutions are discussed. Approximate analytic solutions are found for the cases in which (i) the particle is released from rest with respect to the lab frame and, (ii) the particle is released from rest with respect to the turntable. The equations are then solved numerically to get a more complete understanding of the motion. It is found that one can define an escape speed for the particle which is the minimum speed required to get the particle to move off to infinity. The escape speed is a function of the distance from the center of the turntable and for a given distance from the center, it depends on the direction of initial velocity. A qualitative explanation of this behavior is given in terms of the fictitious forces. Numerical study also indicates an alternative way for measuring the coefficient of friction between the particle and the turntable.
