带棱角物体于斜面上静止释放瞬时将如何运动?

HOW WILL AN OBJECT RESTING ON AN INCLINED PLANE WITH A POINTED END MOVE?

本文研究的问题是斜面上物体的运动,物体以一个棱角与斜面接触,且初始时刻物体处于静止状态。物体有滑动和转动(即物体发生倾倒)两个基本运动类型,总共有九个组合,本文预言了可以出现的运动形式,并给出了对应的发生条件。本问题分析的关键在于摩擦力和质量分布。物体质心如果处于支持力作用线靠近斜面顶部一侧,只能发生向上和向下无滑倾倒(即绕接触点的纯转动)、下滑上倾和下滑下倾运动。物体质心如果处于支持力作用线靠近斜面底部一侧,只能发生向下无滑倾倒、下滑下倾和下滑上倾运动。本问题在教学上很有价值,能给学生带来对科学研究的初步体验。

An object with a pointed edge on an inclined plane at rest initially will have a variety of possible types of motion. The basic motions are sliding and rotation. There are 9 types of motion in total. The paper predicts what can actually happen, and presents the conditions for each type of motion. Our analyses show that the key factors influencing the dynamics of the object are the friction and the mass distribution. For objects with the center of mass locating on the top side of the inclined plane with respect to the pointed edge of the object, only the pure backward or forward rotation happens, sliding down combining with backward or forward rotation. If the center of mass is on the base side of the inclined plane, the object on the inclined plane will have a pure forward rotation or slide down as it rotates backward or forward. The problem can be used for teaching purposes to bring the students with the first taste of research.