【作者】 李艳华； 王新顺； 韩艳华； 毛晓芹； 于战华；

【Author】 LI Yanhua;WANG Xinshun;HAN Yanhua;MAO Xiaoqin;YU Zhanhua;Department of Optoelectronic Science, Harbin Institute of Technology (Weihai);Department of Mathematics, Harbin Institute of Technology (Weihai);

【机构】 哈尔滨工业大学(威海)光电科学系； 哈尔滨工业大学(威海)数学系；

【摘要】 均质半球壳质心位置求解是大学物理教材中的一道典型例题,教材选取最佳质量微元,在球坐标系下计算质心位置,方法简单、直接。本文针对学生分析该问题中易出现的分析误区对半球壳质心位置求解问题进行了详细研究,从微积分思想出发给出解析分析。首先,利用第一型曲面积分,在直角坐标系下给出了均质半球壳质心位置求解的计算方法;其次,在球坐标系下,分析了大学物理教材均质半球壳质心位置求解的合理性和有效性;最后,利用曲线旋转法,通过旋转体的侧面积微元求得半球壳的质心位置。分析过程充分展示了微元法分析半球壳质心位置求解的严谨逻辑及物理思想处理问题的精妙,促进数学、物理学科的知识融合,培养学生的研究性思维及发散性创新思维。更多还原

【Abstract】 Solving the centroid position of a homogeneous hemispherical shell is a typical example in college physics textbooks.The best quality microelement is selected to calculate the centroid position in a spherical coordinate system,The method is simple and direct.In this paper,the problem of solving the centroid position of a hemispherical shell is studied in detail,aiming at the analysis errors that students often encounter in analyzing the problem,the analytical analysis is given from the thought of calculus.Firstly,using the first type surface integral,the calculation method of the position of the hemispherical shell centroid is given in Cartesian coordinate system;Secondly,the rationality and effectiveness of the analysis of the centroid position of the hemispherical shell in college physics textbook are given;Finally,using the curve rotation method,the centroid position of of a homogeneous hemispherical shell is calculated by calculating the side area microelement of the rotating body.The whole analytical process fully shows the rigorous logic of analyzing the centroid position of the hemispherical shell using the microelement method and the ingenuity of solving problems using the physics idea,promoting the integration of knowledge in mathematics and physics,and cultivating students’ research thinking and divergent innovative thinking.更多还原