Moment of inertia

About: Moment of inertia is a research topic. Over the lifetime, 6518 publications have been published within this topic receiving 103129 citations. The topic is also known as: mass moment of inertia.

Neutron Star Structure and the Equation of State

Abstract: The structure of neutron stars is considered from theoretical and observational perspectives We demonstrate an important aspect of neutron star structure: the neutron star radius is primarily determined by the behavior of the pressure of matter in the vicinity of nuclear matter equilibrium density In the event that extreme softening does not occur at these densities, the radius is virtually independent of the mass and is determined by the magnitude of the pressure For equations of state with extreme softening or those that are self-bound, the radius is more sensitive to the mass Our results show that in the absence of extreme softening, a measurement of the radius of a neutron star more accurate than about 1 km will usefully constrain the equation of state We also show that the pressure near nuclear matter density is primarily a function of the density dependence of the nuclear symmetry energy, while the nuclear incompressibility and skewness parameters play secondary roles In addition, we show that the moment of inertia and the binding energy of neutron stars, for a large class of equations of state, are nearly universal functions of the star's compactness These features can be understood by considering two analytic, yet realistic, solutions of Einstein's equations, by, respectively, Buchdahl and Tolman We deduce useful approximations for the fraction of the moment of inertia residing in the crust, which is a function of the stellar compactness and, in addition, the pressure at the core-crust interface

Uniqueness in the Inversion of Inaccurate Gross Earth Data

Abstract: A gross Earth datum is a single measurable number describing some property of the whole Earth, such as mass, moment of inertia, or the frequency of oscillation of some identified elastic-gravitational normal mode. We suppose that a finite set G of gross Earth data has been measured, that the measurements are inaccurate, and that the variance matrix of the errors of measurement can be estimated. We show that some such sets G of measurements determine the structure of the Earth within certain limits of error except for fine-scale detail. That is, from some setsG it is possible to compute localized averages of the Earth structure at various depths. These localized averages will be slightly in error, and their errors will be larger as their resolving lengths are shortened. We show how to determine whether a given set G of measured gross Earth data permits such a construction of localized averages, and, if so, how to find the shortest length scale over which G gives a local average structure at a particular depth if the variance of the error in computing that local average from G is to be less than a specified amount. We apply the general theory to the linear problem of finding the depth variation of a frequency-independent local elastic dissipation ( Q ) from the observed damping rates of a finite number of normal modes. We also apply the theory to the nonlinear problem of finding density against depth from the total mass, moment and normal-mode frequencies, in case the compressional and shear velocities are known.

The solid molecular hydrogens in the condensed phase: Fundamentals and static properties

Abstract: The molecular hydrogens (${\mathrm{H}}_{2}$, ${\mathrm{D}}_{2}$, HD, etc.) form the simplest of all molecular solids. The combination of the light mass, small moment of inertia, weak interactions, and the quasi-metastable ortho-para species result in a fascinating low-temperature behavior that can be understood to a large extent from considerations of first principles. After discussing single molecule properties and intermolecular interactions we discuss in detail the ortho-para properties, conversion and diffusion. This is followed by a description of the crystal structures and the orientational ordering phenomena. The thermodynamic properties are reviewed. The article is concluded with a discussion of the translational ground state of the solid and the effect of the large zero-point motion on the solid state properties. A large number of data are collected in tables and graphs to provide a reference source.

Determination of Molecular Structures from Ground State Rotational Constants

Abstract: Kraitchman has shown that a single isotopic substitution on an atom is sufficient to determine directly the coordinates of that atom with respect to the principal axes of the original molecule. Kraitchman's formulas represent exact solutions of the equations for the equilibrium moments of inertia. However, the effects of the zero‐point vibrations are such that the coordinates obtained by substitution from the ground state moments of inertia I0 are systematically less than r0. These coordinates have here been called r (substitution) or rs, and it is found that rs≃(r0+re)/2, and Is= ∑ imirsi2≃(I0+Ie)/2.In the usual method of solution, the coordinate of one atom is determined from the equation for I0, and therefore the difference I0—Is must be made up by this one coordinate. This introduces a large error in the structures normally determined from ground state constants, and results in variations of 0.01 A in structures determined from different sets of isotopic species. If instead, we obtain the structure on...

Energy Levels and Thermodynamic Functions for Molecules with Internal Rotation I. Rigid Frame with Attached Tops

Abstract: A general treatment of internal rotation is given for molecules whose moments of inertia for over‐all rotation are independent of internal rotational coordinates. Tables are presented for the various thermodynamic functions which are accurate for molecules with one internal rotation and for the potential energy (V/2) (1 — cos nφ). The tables are shown to be a good approximation for molecules with several internal rotational coordinates, provided the potential energy can be expressed as a sum of terms of this type. Methods are suggested for treating problems where cross terms involving more than one internal coordinate are present in the potential energy. The energy level expressions are developed for the more general case with the potential energy expressed by a Fourier series. Although a few specific cases were worked out with different shape potential barriers, it appears that the simple form assumed above will be satisfactory for many purposes.