-转动惯量及其计算方法

-转动惯量及其计算方法

渤海大学本科毕业论文（设计）

转动惯量及其求法

The Computing Method of Moment of Inertia

学院（系）：数理学院

专业：物理师范

学号：12022004

学生姓名：郝政超

入学年度：2012

指导教师：王春艳

完成日期：2016年3月21日

渤海大学

Bohai University

摘要

随着科学与技术的飞速发展，刚体的转动惯量作为一个十分重要的参数，使他在很多领域里受到了重视，尤其是工业领域。近几年来，伴随着高科技的飞速发展，关于刚体转动惯量的研讨，尤其是对于那些质地不均匀和形状不规则刚体的转动惯量的深入探究，已经全然对将来的军事、航空、以及精密仪器的制作等行业产生了极为深远的影响。本篇文章将在这些知识基础上，遵循着循序渐进的原则，对常见刚体的转动惯量以及不同常见规则的刚体的转动惯量的计算进行深入的研究。

本文主要分为四个部分。首先本文系统介绍了刚体以及刚体的动量矩，转动动能和转动惯量的基础知识。其次介绍了刚体的平行轴定理和垂直轴定理，并且给出了转动惯量常见的的计算方法。接着，本文介绍了几类常见的刚体的转动惯量，其中包括圆环、圆柱体、圆盘、杆、空心圆柱体以及六面体的转动惯量。最后，通过具体实例给出了不规则刚体的转动惯量的测量方法。

【关键词】力矩；角加速度；摩擦力

The compute of moment of inertia

Abstract

Delve into the irregular inhomogeneous along with the science and technology rapid development, the rigid body rotational inertia is a very important parameter, make him in many fields by the attention, especially industrial fields. In recent years, along with the high-tech rapid development of rigid body rotation inertia of research, especially for those texture and shape of rigid body inertia has been completely to the future military, aviation, and precision instrument manufacturing industry produced extremely far-reaching impact. This article will be in the knowledge base, follow the gradual principle of common rigid body inertia and common rules of rigid body rotation The calculation of inertia is deeply studied.

This paper is divided into four parts. First of all, this paper systematically introduced the rigid body and the angular momentum of a rigid body, rotational kinetic energy and rotational inertia based knowledge. Followed by the introduction of the parallel axis theorem of rigid body and vertical axis theorem, and gives the rotation inertia common calculation method. Then, this paper introduces the several common types of rigid body's moment of inertia, which include ring, cylinder, disc, rod, hollow cylinder and hexahedron of the moment of inertia. Finally, through specific examples are given irregular rigid body rotational inertia measurement method.

Key Words：Moment；Angular Acceleration；Friction

目录

摘要 ................................................................................................................................. Abstract ................................................................................................................................. I 引言 . 0

1刚体的转动惯量 (9)

1.1转动惯量的定义与物理意义 (1)

1.2刚体的动量矩 (1)

1.3刚体的转动动能与转动惯量 (3)

2 转动惯量的相关定理及计算方法 (8)

2.1刚体的平行轴定理 (7)

2.2刚体的垂直轴定理与伸展定则 (7)

2.3转动惯量的计算方法 (7)

3 常见刚体的转动惯量 (9)

3.1圆环的转动惯量 (9)

3.2圆柱体的转动惯量 (10)

3.3圆盘的转动惯量 (11)

3.4杆的转动惯量 (12)

3.5空心圆柱及六面体的转动惯量 (12)

4不规则刚体转动惯量的测量 (14)

4.1实验方法测量 (14)

4.2对刚体的转动惯量的误差分析 (15)

参考文献 (18)