三线摆实验中用大摆角测量转动惯量  

Measuring the moment of inertia using trifilar pendulum with large rotation angle

作　　者：周艳明 翦知渐 谢中 ZHOU Yan-ming;JIAN Zhi-jian;XIE Zhong(College of Physics and Electronics Science, Hunan University, Changsha 410082, China)

机构地区：[1]湖南大学物理与微电子科学学院大学物理实验中心,湖南长沙410082

出　　处：《物理实验》2020年第10期22-27,46,共7页Physics Experimentation

摘　　要：利用智能手机APP的陀螺仪传感器可以获得三线摆运动过程中角速度的运动轨迹.对测量数据分析发现初始摆角很小时三线摆周期的测量数据不一定可靠,这与传统测量方法强调的小角度转动有出入.通常对大角度摆动的周期修正基于测出的初始摆角,但一般实验室中不易对其进行准确测定而难以应用于实际测量中.通过测量多个不同初始摆角测量的最大振幅及对应周期,再对振幅与周期相关数据进行多项式拟合,得到初始摆角趋于零的最佳周期值T0.运用此法测量标准圆环的转动惯量,由T0值获得的转动惯量测量结果与理论值比较精度优于0.2%.By using the gyroscope sensor and APP of smart phone,the angular velocity curve of trifilar pendulum could be obtained,which was impossible in the traditional method.Through the analysis and processing of the measurement data,it was found that for very small initial rotation angle,the data of the period might be unreliable,which was conflicted with the small angle rotation emphasized by the traditional method.The periodic correction of large rotational angle was usually based on the measured initial rotation angle,which was not easy to measure accurately in general laboratory.A new method of implement the experiment and data processing was proposed.By measuring the maximum amplitude and the corresponding period of series large rotation angles,and then fitting the data by polynomial,the optimal periodic value T0 when the initial rotation angle tending to zero was obtained.The moment of inertia of standard ring was measured by this method.Compared with theoretical values,the deviation were less than 0.2%.

关 键 词：三线摆 小角度近似 大摆角 周期修正 

分 类 号：O313.3[理学—一般力学与力学基础]