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.

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.

Determination of the Buckling Load of Struts with Successive Approximations

1943 ◽  
Vol 47 (387) ◽  
pp. 103-105
Author(s):  
J. Ratzersdorfer
Keyword(s):  
Differential Equation ◽  
Compressive Force ◽  
Buckling Load ◽  
Moment Of Inertia ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Exact Determination ◽  
The Moment ◽  
Image Position

In cases of tapered struts with hinged or built-in ends where the exact determination of the buckling load is complicated it may be useful to apply a method of successive approximations.Let us first consider a bar of the length l with hinged ends under the action of the compressive force P. The differential equation of the bending line becomeswhere v is the deflection at the section u, v with the moment of inertia I (u) and E is Young's modulus. At the ends of the bar the deflection v is equal to zero (Fig. I).

Experimental Determination of the Moment of Inertias of USM e-UAV

2013 ◽  
Vol 465-466 ◽  
pp. 368-372
Author(s):  
M. Haniff Junos ◽  
Nurulasikin Mohd Suhadis ◽  
Mahmud M. Zihad
Keyword(s):  
Experimental Data ◽  
Experimental Determination ◽  
Moment Of Inertia ◽  
Experimental Setup ◽  
Torsion Pendulum ◽  
The Moment ◽  
Pendulum Experiment

This paper presents the experimental determination of the moment of inertia of USM e-UAV by using pendulum method. Compound pendulum experiment is used to determine the moment of inertia about x and y axes while the moment of inertia about z-axis is determined using bifilar torsion pendulum method. An experimental setup is developed with appropriate dimension to accommodate USM e-UAV. Experimental data are presented and discussed.

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.

Note on the reduction of Mr. Crookes’s experiments on the decrement of the arc of vibration of a mica plate oscillating within a bulb containing more or less rarefied gas

1881 ◽  
Vol 31 (206-211) ◽  
pp. 458-460
Keyword(s):  
Rarefied Gas ◽  
Mathematical Problem ◽  
Moment Of Inertia ◽  
Mica Plate ◽  
The Moment ◽  
Coefficient Of Viscosity

The determination of the motion of the gas within the bulb, which would theoretically lead to a determination of the coefficient of viscosity of the gas, forms a mathematical problem of hopeless difficulty. Nevertheless we are able, by attending to the condition of similarity of the motion in different cases, to compare the viscosities of the differen t gases for as many groups of corresponding pressures as we please. Setting aside certain minute corrections, which would have vanished altogether had the moment of inertia of the vibrating body been .sufficient to make the time of vibration sensibly independent of the gas, as was approxim ately the case, the condition of sim ilarity is th at the densities shall be as the log decrements of the arc of vibration, and the conclusion from theory is th at when th a t condition is satisfied, then the viscosities are in the same ratio.

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