摘要
扭摆法测量转动惯量是大学物理实验中一个重要的项目.现行物理实验教材中,其相对误差分析通过对比转动惯量理论值与实验测量值得到,这种处理方式值得商榷.本文针对这一问题,采用不确定度计算,分别讨论了转动惯量的理论值与实验值的不确定度公式,并比较了两种转动惯量计算结果的差别,分析其产生的可能原因.并提出了用线性拟合作图法验证平行轴定理的新思路,根据微扰理论提出了得到扭转常数与摆幅相互关系的测量方案和减少误差的处理途径.最后用数值计算讨论了同时考虑摩擦阻力和扭转常数随摆角变化对摆动周期的影响.
The application of torsion pendulum to measure the rotational inertia is an impor- tant project in college physics experiment. In most of current experimental instructor book, the relative error calculation is obtained by comparing the theoretical value of rotational inertia and the experimental data. This approach is questionable. In this paper, the formula of uncer- tainty of torsion pendulum is given to calculate the theoretical uncertainty and the experimen- tal ones, respectively. Differences between the theorical results and experimental data are compared with the analysis of the possible reason. A new way to verify the parallel axis theo- rem is provided through graphing method of linear fitting. Meanwhile, a new method is pro- moted to obtain the relationship between the coefficient of torsional pendulum and the rota- tional angle amplitude based on the perturbation theory, which leads to the possibility of re- duction of errors in experiments. At last, numerical calculations are given to discuss how the oscillating period is affected by the frictional resistance and the changing torsional coefficient with the pendulum angle at the same time.
出处
《物理与工程》
2016年第1期46-50,共5页
Physics and Engineering
关键词
扭摆
转动惯量
不确定度
数据处理
误差
torsional pendulum
rotational inertia
uncertainty
data processing
error
