New Theorems for Moments of Inertia

1993 ◽  
Vol 21 (4) ◽  
pp. 355-366 ◽  
Author(s):  
David L. Wallach
Keyword(s):  
Regular Polygon ◽  
Moment Of Inertia ◽  
Regular Polygons ◽  
Centre Of Mass ◽  
Moments Of Inertia ◽  
The Moment

The moment of inertia of a plane lamina about any axis not in this plane can be easily calculated if the moments of inertia about two mutually perpendicular axes in the plane are known. Then one can conclude that the moments of inertia of regular polygons and polyhedra have symmetry about a line or point, respectively, about their centres of mass. Furthermore, the moment of inertia about the apex of a right pyramid with a regular polygon base is dependent only on the angle the axis makes with the altitude. From this last statement, the calculation of the centre of mass moments of inertia of polyhedra becomes very easy.

A Project in the Determination of the Moment of Inertia

2005 ◽  
Vol 33 (4) ◽  
pp. 319-338
Author(s):  
Ron P. Podhorodeski ◽  
Paul Sobejko
Keyword(s):  
Dynamic Properties ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Moment Of Inertia ◽  
Educational Goal ◽  
Centre Of Mass ◽  
Comparison Of Results ◽  
Physical Testing ◽  
The Moment

Analysis of the forces involved in mechanical systems requires an understanding of the dynamic properties of the system's components. In this work, a project on the determination of both the location of the centre of mass and inertial properties is described. The project involves physical testing, the proposal of approximate models, and the comparison of results. The educational goal of the project is to give students and appreciation of second mass moments and the validity of assumptions that are often applied in component modelling. This work reviews relevant equations of motion and discusses techniques to determine or estimate the centre of mass and second moment of inertia. An example project problem and solutions are presented. The value of such project problems within a first course on the theory of mechanisms is discussed.

Increasing the Moment of Inertia of Crane Rails Torsional

2017 ◽  
Vol 865 ◽  
pp. 188-191
Author(s):  
Kirill Nezdanov ◽  
Igor Garkin ◽  
Nikolay Laskov
Keyword(s):  
Economic Benefits ◽  
Cross Sectional Area ◽  
Moment Of Inertia ◽  
High Moment ◽  
Operating Costs ◽  
Sectional Area ◽  
Cross Sectional ◽  
Moments Of Inertia ◽  
Section Profile ◽  
The Moment

This article is devoted to extreme increase in the moments of inertia of crane rails torsional strongly influence the endurance of crane girders. We investigate increase in moment of inertia of the rail under torsion with increasing thickness of the walls and shelves of thick-walled I-section profile in the square until its transformation into a square profile. It was found that the transformation of the profile of a monolithic solid square increases the moment of inertia of the torsion Jkr, cm4 to 3,1075 times and reaches its extreme. A cross-sectional area remains constant (const). Crane rails with a high moment of inertia for torsion provides significant economic benefits, and significantly reduces the operating costs of the enterprise.

The Inertial Effect in Rotational Fluorescence Depolarization

1992 ◽  
Vol 47 (9) ◽  
pp. 971-973 ◽  
Author(s):  
A. Kawski ◽  
P. Bojarski ◽  
A. Kubicki
Keyword(s):  
Empirical Equation ◽  
Molecular Geometry ◽  
Moment Of Inertia ◽  
Experimental Results ◽  
Inertial Effect ◽  
Fluorescence Depolarization ◽  
Moments Of Inertia ◽  
Low Viscosity ◽  
The Moment ◽  
Semi Empirical

Abstract The influence of the moment of inertia on the rotational fluorescence depolarization is discussed. Based on experimental results obtained for five luminescent compounds: 2,5-diphenyloxazole (PPO), 2,2'-p-phenylene-bis(5-phenyloxazole) (POPOP), p-bis[2-(5-α-naphthyloxazolyl)]-benzene (α-NOPON), 4-dimethylamino-ω-methylsulphonyl-trans-styrene (3a) in n-parafines at low viscosity (from 0.22 x 10-3 Pa • s to 0.993 x 10-3 Pa • s) and diphenylenestilbene (DPS) in different solvents, a semi-empirical equation is proposed, yielding moments of inertia that are only two to five times higher than those estimated from the molecular geometry

Dealing with varying moments of inertia of girders in bridge analysis

1988 ◽  
Vol 15 (2) ◽  
pp. 232-239 ◽  
Author(s):  
Baidar Bakht ◽  
Leslie G. Jaeger
Keyword(s):  
Load Distribution ◽  
Moment Of Inertia ◽  
Moments Of Inertia ◽  
Finite Strip ◽  
Girder Bridges ◽  
Grillage Analysis ◽  
Computer Based ◽  
Manual Methods ◽  
The Moment

In many slab-on-girder bridges, especially those that are continuous over two or more spans, the moment of inertia of a girder varies significantly along the length of the bridge. This paper critically examines the practice of analyzing such bridges for load distribution by methods that make the assumption of constant longitudinal torsional and flexural rigidities. It is found that this practice may not be valid for those slab-on-girder bridges in which variations of the girder moments of inertia are very large.A recommended procedure is given for cases in which the variation in moment of inertia is not too severe. The procedure involves (a) the determination of total bending moments, treating the bridge as a beam of variable moment of inertia, and (b) the determination of an equivalent constant moment of inertia for beams of varying moment of inertia. Using this procedure the load distribution properties of the bridge can be realistically analyzed by those computer-based methods (e.g., orthotropic plate, finite strip, and semicontinuum methods) or manual methods (e.g., AASHTO and Ontario methods) that cannot directly take account of the variation of longitudinal flexural rigidity.The validity of the recommended procedure is established by comparing its results with those of the grillage analysis method that does take account of the variation of the girder moment of inertia. Key words: bridge analysis, girders, load distribution, slab-on-girder bridges.

Trägheitsmomente nach Inglis und das Bohr-van-Leeuwensche Theorem

1960 ◽  
Vol 15 (5-6) ◽  
pp. 371-377
Author(s):  
Gerhart Lüders
Keyword(s):  
Rigid Rotation ◽  
Moment Of Inertia ◽  
Interacting Particles ◽  
Theoretical Determination ◽  
General Validity ◽  
Moments Of Inertia ◽  
Deformed Nuclei ◽  
The Moment

It has been stated by BOHR and MOTTELSON that INGLIS’ method for the theoretical determination of moments of inertia of deformed nuclei, in the limit of a great number of non-interacting particles leads to the moment of inertia of rigid rotation. Recently doubts have been raised regarding the general validity of this statement. In the present paper the proof of the assertion is given in detail and its relation to the BOHR-VAN-LEEUWEN theorem is discussed.

Moments of Inertia of Bat Wings and Body

1991 ◽  
Vol 158 (1) ◽  
pp. 19-35 ◽  
Author(s):  
MIKAEL THOLLESSON ◽  
ULLA M. NORBERG
Keyword(s):  
Body Mass ◽  
Shoulder Joint ◽  
Mean Value ◽  
The Body ◽  
Moment Of Inertia ◽  
Moments Of Inertia ◽  
Wing Span ◽  
The Mean ◽  
Roll Axis ◽  
The Moment

The moments of inertia of the wings about the shoulder joint and about the roll axis were estimated in eight species of bats, using strip analysis. The moment of inertia of the bat's trunk about the roll axis was estimated by assuming the body and head to be ellipsoids. The slopes of the regressions of moment of inertia of one wing about the shoulder joint (Jw) versus body mass (mtot), wing span (b) and wing area (S) were as expected for geometrically similar animals of different size. The exponent for Jwversus body mass in bats deviates from that found for birds, while the exponent for Jw versus wing span does not. A multiple regression was used to show that Jw may be estimated by: J w = 4.49 × 10−3mtot0.53b2.15S0.65. The mean value of the moment of inertia originating from the trunk is 7 % of the bat's total moment of inertia (of wings and body combined) about the roll axis. The mass of one wing (mw) was plotted against body mass for the eight bat species, which gives: m w = 0.112mtot1 11. The slope for our bats, 1.11, is similar to that obtained for birds, 1.10. Adaptations to reduce the moments of inertia may be more important for increasing a bat's flight agility (roll acceleration) than for decreasing the total mechanical power required to fly. The influences of wing moment of inertia and wing shape on manoeuvrability and agility are discussed.

scholarly journals The program «Moments of inertia» for calculating the moments of inertia of the rotational motion of molecules

2019 ◽  
Vol 57 (3) ◽  
pp. 42-50
Author(s):  
Mikhail N. Koverda ◽  
◽  
Eugeny N. Ofitserov ◽  
Anna A. Koverda ◽  
◽  
...  
Keyword(s):  
Rotational Motion ◽  
Dimensional Space ◽  
Center Of Mass ◽  
Three Dimensional ◽  
Carbon Chain ◽  
Moment Of Inertia ◽  
Structure Property ◽  
Moments Of Inertia ◽  
Simple Molecules ◽  
The Moment

The moment of inertia of the rotational motion I, as a descriptor of the spatial structure of the molecule, which determines the properties of a substance, in accordance with the works of recent years, begins to acquire significance in the study of the «structure – property» dependencies, allowing one to describe the change in the properties of compounds in homologous series and address odd homologues. The problem is that there is no universal and transparent method for calculating the moments of inertia of the rotational motion of molecules. Researchers are trying to solve this problem in various ways: presenting the molecule as its carbon chain and calculating the moments of inertia only for it, neglecting the contribution of other atoms, manually calculating the moments of inertia for small simple molecules, based on their estimated geometry, extracting intermediate results from quantum chemical calculations of the program packages like Gaussian or Gamess. We have developed a program for the exact calculation of the moments of inertia, which uses the specification of the exact geometry of the molecule in three-dimensional space using Cartesian coordinates. The program is written on Perl programming language and is available under the GNU General Public License v3.0 (free software). The program uses XYZ files as input data. The principle of the program is to iteratively calculate the inertia moments for all possible positions in the space of the axis of rotation passing through the center of mass of the calculated molecule. The minimum and maximum values of the moments of inertia obtained during the calculation correspond to two perpendicular axes of rotation of the molecule (x and z). The moment of inertia with respect to the third remaining y axis is calculated after finding the canonical equation of the straight axis perpendicular to the found x and z axes.

Dynamic rotational characteristics of actinides on empirical approach

Open Physics ◽  
2008 ◽  
Vol 6 (3) ◽  
Author(s):  
Maria Kaczmarczyk ◽  
Andrzej Korejwo
Keyword(s):  
Experimental Data ◽  
Angular Momentum ◽  
Ground Level ◽  
Analytical Form ◽  
Moment Of Inertia ◽  
Relative Deviation ◽  
Moments Of Inertia ◽  
Rotational States ◽  
The Moment ◽  
Experimental Values

AbstractIn the paper calculation of the moments of inertia for nuclei from the region 87 ≤ Z ≤ 100 and 130 ≤ N ≤ 156 was made in dependence on the angular momentum of their rotational states. The experimental values of the moments of inertia were calculated for rotational energy of the classic rotor in its quantum form, with the use of a simple formula. The moment of inertia term appearing in the formula was treated as a variable. The calculations were carried out on the basis of experimental data for the energies of the rotational levels for 51 bands built on ground states for even-even nuclei and for nuclei with odd mass number A. In addition, 30 rotational bands built on excited states were also analysed in the investigated region in case of even-even nuclei. For many bands and nuclei the considered dependence of the moment of inertia on angular momentum has been found in the analytical form by fitting polynomials to the experimental data. It turned out that obtained results for the moments of inertia made it possible to describe the energies of rotational levels with a relative deviation not greater or only slightly greater than 1%. In general, in the case of 12 bands of ground level the maximum relative deviation of obtained level energies is smaller than 1%.

Perception of the moment of inertia of hand tools

1982 ◽  
Author(s):  
Carol Zahner ◽  
M. Stephen Kaminaka
Keyword(s):  
Moment Of Inertia ◽  
Hand Tools ◽  
The Moment
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