物体转动惯量三线摆测量方法的若干为题研究-毕业论文网

论文总字数：17084字

目录

摘要..............................................1

课题及研究背景.........................................3
实验原理........................................3
公式推导........................................4
实验仪器数据....................................6
误差分析........................................6

5.1偶然误差和系统误差对误差的影响.......................................6

5.2 摆角对误差的影响....................................................7

5.3 摆线长度对误差的影响...............................................11

5.4 所测圆环质量对误差的影响...........................................16

5.5 空气阻尼对实验的影响...............................................19

6.总结..................................................23

参考文献.............................................24

致谢....................................................26

三线摆测量物体转动惯量的研究

张耀文

，China

Abstract:Moment of inertia is a measure of the inertia of an object's rotation, and its size depends on several factors of the object, the mass of the object, the mass distribution, the shape of the object and the position of its axis. There is no doubt that the physical significance of the inertia of an object is a very important parameter in scientific experiments, aerospace, machinery, engineering, and even the industrial field. The three-wire pendulum has the advantages of simple structure, convenient operation and convenient use, and is convenient for students to use. But relatively speaking, the result of the measurement error is larger. In this paper, the qualitative and quantitative analysis of the influence error factors in the experiment of measuring the rotational inertia of the object by three wire pendulum method is carried out. It is found that the factors influencing the final error are classified into five categories.Respectively: experimental instruments bring system error and accidental error can not be avoided; influence of air resistance on the measurement results is negligible; the swing angle in the five to fifteen degrees on the measurement results are not greatly affected, but too small or too large will cause the error increases; the cycloid length is longer, the higher the accuracy of the experiment；The larger the mass of the object to be measured, the smaller the error of the resulting result.The factors that cause the error are summarized, and the conclusion that how to control these factors to minimize the experimental error is obtained.

Key word: moment of inertia; Three wire pendulum method; error factor;

课题及研究背景

转动惯量是刚体绕轴转动时惯性大小的一个量度。转动惯量有着非常重要的物理意义，在工程技术、科学实验、航天、机械、电力、仪表等工业领域也是一个非常重要的参量。比如在发动机叶片、陀螺、飞轮以及人造卫星的外形设计上，对转动惯量的精确地测定，都是十分必要的。

三线摆测刚体转动惯量实验^[1-3]思想清晰、实验方法简单、测量的结果好等种种原因，一直是大学物理的重要实验^[4-6]，但其测量公式推导中用到了几项参量的近似值，所以必然对实验的系统误差会造成一定的影响，本文对此进行定量的分析，阐明其对实验结果的影响。所得到的结论可对实验教学提供数据参考。

2. 实验原理

三线摆实验装置采用的是FB210A型三线摆组合实验仪器和FB213A型数显计时计数毫秒仪器，外形如图3.1所示。

图1 FB210A三线摆组合实验仪器

如上图所示，上，下两个悬盘在做实验时必须处于水平的状态，并将两悬盘悬挂在仪器的横梁上。两个圆盘用相同材料的同样长的悬线相链接。将上圆盘固定在横梁保持稳定，下圆盘可以绕仪器的中心轴OO’作小摆角的摆动运动。因为下悬盘来回摆动的周期与其转动惯量的大小有关，所以，悬挂的物体不同，转动惯量也就会有所不同，与其相应的摆动周期也将发生相应的变化。