对量纲法求分形物体转动惯量的再思考

指出数学上无穷阶的分形与物理上可实现的有限阶分形物体之间的差别.利用n阶分形三角形与n-1阶分形三角形的相似性,根据标度变换和量纲分析法,得到n阶分形三角形转动惯量的递推公式,进而得到转动惯量的最终表达式.该结果在n趋向无穷大时与无穷阶分形物体的结果一致.     

基于迭代法对分形物体转动惯量的研究

研究具有分形形态的物体绕定轴的转动惯量,以科赫雪花曲线所围图形为例,给出其绕过形心的某固定轴转动惯量的迭代算法和公式.所得结果与已有文献的精确结果完全一致.所提方法步骤明确,便于编程,且适合于一些推广的分形图形.     

分形物体转动惯量的计算

由分形物体的自相似性,给出了推广雪花曲线的质心和转动惯量.     

平面质点系绕质心轴转动惯量的一个定理及应用

提出如下定理:平面质点系对过质心且与质点系所在平面垂直轴的转动惯量在数值上等于任意两质点的质量与它们距离平方乘积之和除以质点系的总质量.该定理不需要确定质点系质心的位置,而是基于各质点间连线距离.给出该定理在杆系和板问题中的若干应用,如多边形杆边框、杆板混合结构、分形板等.所给定理具有一定的理论意义和实用价值.     

关于“用转动惯量仪测物体转动惯量”实验的疑问

用转动惯量仪测量物体转动惯量,是普通物理实验中,最简单的一种测转动惯量方法.这里所说的是圆盘状物体对其中心轴的转动惯量.(参见人民教育出版社1981年出版的华中工学院、天津大学、上海交大编《物理实验》).它的原理和操作简单、现象直     

复摆方程的一种求解方法

利用复摆测量物体的转动惯量是一种重要方法,本文对复摆的转动惯量公式进行拉普拉斯变化,用能量和时间来表达转动惯量,丰富了不规则物体转动惯量的测量方法.     

匀质三角形板和边框的转动惯量

质量均匀分布的物体相对质心轴的转动惯量,通常是由它的几何量表示,这称为转动惯量的几何表示．如果给定物体的顶点坐标,它相对任意轴的转动惯量可以由这些顶点坐标表示,这称为转动惯量的代数表示．由转动惯量的平行轴定理,得到杆和三角形板相对任意转轴转动惯量的代数表示．作为简单应用,得到三角形边框相对质心轴转动惯量的几何量表示．     

切变模量和转动惯量实验的改进

设计了一种基于垂直轴定理的新型吊钩,对切变模量和转动惯量实验进行了改进,使之成为既可测定金属丝切变模量和环、柱等刚体的转动惯量,又可验证反映转动惯量重要性质的平行轴定理及垂直轴定理的多功能实验仪.     

利用恒力矩转动法验证刚体转动惯量正交轴定理

利用恒力矩转动法测量了自制的不锈钢矩形薄板状样品的转动惯量.沿长、宽,和垂直于板面3个方向的转动惯量分别是7.70×10~(-4) kg·m~2,3.23×10~(-3) kg·m~2和3.97×10~(-3) kg·m~2.沿长、宽方向的转动惯量之和基本等于垂直于板面方向的转动惯量,相对偏差仅为0.84%,验证了刚体转动惯量正交轴定理.分析了由薄板厚度对长、宽方向的转动惯量贡献不超过5‰,在实验中无须考虑厚度的影响.测量结果表明:固定螺丝、定位销对测量结果影响不大.此外还分析了空气阻尼、塔轮半径和砝码质量等因素对实验结果的影响.     

刚体转动惯量的质量投影法

根据转动惯量的定义,提出了计算转动惯量的质量投影法,应用质量投影法讨论了六面体、椭圆盘、圆柱、圆台等几种特殊形状均质刚体对转轴的转动惯量.     

中子星的转动惯量与表面红移的研究

在温度、密度及同位旋相关的核物质状态方程的基础上,通过求解Tolman–Oppenheimer–Volkoff方程,得到了中子星的转动惯量与表面红移.计算结果表明,中子星的转动惯量较强地依赖于核物质的不可压缩系数与对称能强度系数,而对核子有效质量不太敏感;中子星的表面红移却对对称能强度系数不太敏感,而较强地依赖于不可压缩系数与核子有效质量.     

Description of the Superdeformed Bands in A～190 Region with a Three-Parameter Formula

The q-deformed moment of inertia, formulated by was first introduced as the mechanical moment of inertia of superdeformed (SD) nuclei. The E2 transition γ-ray energies and the dynamical moment of inertia of the lowest-formed bands in Hg, Ph, and TI isotopes are calculated. The calculated results indicate that the SD bands may be described by the ided-rotor with the q-deformed mpment of inertia.     

刚体绕任意轴转动惯量的简便计算

利用微元求和的方法给出几种刚体对于过质心任意轴的转动惯量公式，并由此引出转动惯量与刚体几何对称性的联系，以及与转动惯量有关的几何形体等价性的一些结果．     

On the moment of inertia of a proto neutron star

The influences of σ* and Φ mesons,temperature and coupling constants of nucleons on the moment of inertia of the proto neutron star(PNS) are examined in the framework of relativistic mean field theory for the baryon octet {n,p,Λ,Σ+,Σ0,Σ+,Ξ-,Ξ0} system.It is found that,compared with that without considering σ* and Φ mesons,the moment of inertia decreases.It is also found that the higher the temperature,the larger the incompressibility and symmetry energy coeficient,and the larger the moment of inertia of a PNS.The influence of temperature and coupling constants of the nucleons on the moment of inertia of a PNS is larger than that of the σ* and Φ mesons.     

On the moment of inertia of a quantum harmonic oscillator

An original method for calculating the moment of inertia of the collective rotation of a nucleus on the basis of the cranking model with the harmonic-oscillator Hamiltonian at arbitrary frequencies of rotation and finite temperature is proposed. In the adiabatic limit, an oscillating chemical-potential dependence of the moment of inertia is obtained by means of analytic calculations. The oscillations of the moment of inertia become more pronounced as deformations approach the spherical limit and decrease exponentially with increasing temperature.     

转动惯量平行轴定理验证实验的改进方案

本文介绍了一种刚体转动惯量平行轴定理验证实验的改进方案.该方案通过调节对称放置在承物台上的两个钢柱到仪器转轴的距离来改变系统的转动惯量,使得总转动惯量可以在较大的范围内改变,并且始终保持了系统质量的对称性分布,从而有效地减小了实验的相对误差,提高了实验结果的可信度.     

扭摆系统中扭杆的等效转动惯量——圆柱杆扭转振动的研究

研究扭摆系统中扭杆的质量或转动惯量对扭摆运动的影响,引入一个概念:扭摆系统中扭杆的等效转动惯量.纠正了一些文献在相关问题上的误解.     

Influence of the moment of inertia of the pendulum on the internal friction (loss tangent) measured by free decay

Summary The internal friction (loss tangent) of solids is normally measured, as a function of temperature, with a torsion pendulum operating in free decay. Curves of the internal friction and the oscillation frequency, against temperature, are obtained at various moments of inertia, to extract the parameters characteristic of the relaxation process (relaxation time and strength). In all these experiments only the temperature is considered as an independent variable and the moment of inertia of the pendulum is mainly used to shift the internal friction peaks in the temperature scale. It is pointed out in the paper that the moment of inertia is also an independent variable which can be used to determine, with high accuracy, if the measured peak is of the Debye type or not. A new torsion pendulum, with continuously variable moment of inertia is presented, which allows measurements of the partial derivative of the internal friction and the oscillation frequency with respect to the moment of inertia, at constant temperature. Finally, some measurements of the Snoek relaxation in Nb-O alloys are presented, to show the applicability of the concepts developed in the paper. The authors of this paper have agreed to not receive the proofs for correction.     

Properties of rotational excitations in odd mass Dy isotopes

The data on high-spin rotational states in¹⁵⁵Dy,¹⁵⁷Dy,¹⁵⁹Dy and¹⁶¹Dy are discussed within a model where a particle is coupled to a rotor with a variable moment of inertia. In this model there is often a definite improvement in the quality and stability of the fits to levels in the positive-parity band below spin 25/2 when the moment of inertia of the core exhibits a linear dependence on the square of the rotational angular velocity as compared to the situation where a linear dependence onI(I+1) is assumed. In the improved fits the empirical matrix elements of the Coriolis force exhibit a smooth and significant increase with decreasing moment of inertia. The rotational energies above spin 25/2 in the positive-parity band and above 19/2 in the 11/2^? [505] band are understood within the present theoretical model if the moment of inertia increases more rapidly than the linear trend established at lower spin. In the 11/2^? [505] band this increase follows rather closely the behaviour in the even nuclei whereas in the positive-parity band the curves are quite flat even beyond the point where the moment of inertia in the even nuclei exhibits a discontinuous or back-bending behaviour. The significance of this observation is discussed in the light of existing theories on nuclear moments of inertia.