圆盘转动惯量的三种计算方法

Three methods of calculating the moment of inertia of a disk

刚体的转动惯量是大学物理刚体力学中的重点。研究采用了三种方法计算圆盘形状物体绕中心转动对称轴的转动惯量,即微元定义求解法、量纲分析法和等边n角形极限法。提出了后面两种巧妙的计算方法,引导学生在解决问题的时候开阔思维,激发其学习的积极性及对科研的探索精神。

The moment of inertia of rigid body is the focus of rigid body mechanics in university physics. In this paper, three methods are used to calculate the moment of inertia of a disk-shaped object about a central rotational axis of symmetry, namely, the method of solving the definition of micro element, the method of dimensional analysis and the method of limit of n-angle with equal sides. The last two ingenious calculation methods are put forward to guide students to broaden their thinking when solving problems, stimulate their enthusiasm for learning and explore the spirit of scientific research.