大学物理 ›› 2026, Vol. 45 ›› Issue (6): 57-.doi: 10.16854/j.cnki.1000-0712.250365

• 教学讨论 • 上一篇    下一篇

三个关于质点系的动能定理及两例应用

邵云   

  1. 南京晓庄学院 电子工程学院,江苏南京211171
  • 收稿日期:2025-07-14 接受日期:2025-10-12 出版日期:2026-08-01 发布日期:2026-08-28
  • 作者简介:邵云(1973—),男,江苏镇江人,南京晓庄学院电子工程学院讲师,主要从事力学、热学教学和研究工作.

Three kinetic energy theorems about particle systems and two applications

SHAO Yun   

  1. School of Electronic Engineering, Nanjing Xiaozhuang College, Nanjing, Jiangsu 211171, China
  • Received:2025-07-14 Accepted:2025-10-12 Online:2026-08-01 Published:2026-08-28

摘要: 文章回顾性地证明得出三个关于质点系的动能定理,即惯性(或地面)参考系下质点系的动能定理、关于质心的动能定理、质心参考系下质点系的动能定理,指出它们之间的相互关系,并将它们应用于两个实例,揭示出滑动摩擦力对边滑边滚小球做负功的某些特殊机制.文中还顺带证明了其他的一些熟知的关系式.文章的内容对于基础物理教学、研究、考试,或均有一定的参考和利用价值.

关键词: 质点系的动能定理, 惯性系, 质心系, 质心的动能定理, 滑动摩擦力做功

Abstract: The article retrospectively proves three kinetic energy theorems about particle systems, namely the kinetic energy theorem about particle systems in inertial (or ground) reference frames, the kinetic energy theorem about the center of mass, and the kinetic energy theorem about particle systems in the center of mass reference frame. It points out their interrelationships and applies them to two examples, and reveals some special mechanisms by which sliding friction force do negative work on a rolling and sliding small ball. In the article, some other well-known relational expressions are incidentally proved as well. The content of the article has certain reference and utilization value for basic physics teaching, research, and examinations.

Key words: the kinetic energy theorem of a system of particles, inertial reference frame, centroid reference frame, the kinetic energy theorem of the center of mass, work done by sliding friction force