Sideway
output.to from Sideway
Draft for Information Only

Content

Moment of Inertia of Common Shape
  Moment of Inertia of a Mass of Homogeneous Body
   Moment of Inertia of Slender Rod
   Moment of Inertia of Circular Cylinder
   Moment of Inertia of Rectangular Prism
   Moment of Inertia of Circular Cone
   Moment of Inertia of Sphere

Moment of Inertia of Common Shape

In general, the second moment of mass in space about an axis can be determined by

image

Moment of Inertia of a Mass of Homogeneous Body

Moment of Inertia of Slender Rod

image

Consider a slender homogenous circular rod of length L with uniform cross-sectional area A and homogenouse material density ρ. Both the cross-sectional area and the material density are constant over the lenght. Since the cross-sectional radius r is much smaller than the length of slender rod, the mass and the elemental mass of the slender rod can be expressed in terms of the mass per unit length, if the reference axis lies in centre of gravity of the slender rod, the mass moment of inertia of the slender rod with respect to an centroidal axis can be expressed as the elemental mass on the axial axis with the distance x as the radius between the elemental mass and the reference axis. Imply

image

Moment of Inertia of Circular Cylinder

image

Consider a homogenous circular cylinder of length L with uniform cross-sectional area A of radius r and homogenouse material density l. Both the cross-sectional area and the material density are constant over the lenght, the mass and the elemental mass of the circular cylinder can be expressed in terms of the volume of the circular cylinder. Since the cross-sectional radius r cannot be neglected, the actual distance between the elemental mass and the reference axis should be used. The moments of inertia about axes x and z, can be determined by parallel-axis theorem. Imply

image

And the moments of inertia about axis y can also be determined by parallel-axis theorem. Imply

image

Moment of Inertia of Rectangular Prism

image

Consider a homogenous rectangular prism of length L with uniform cross-sectional area A of height h, width b and homogenouse material density l. Both the cross-sectional area and the material density are constant over the lenght, the mass and the elemental mass of the rectangular prism can be expressed in terms of the volume of the rectangular prism. Since the cross-sectional dimensions cannot be neglected, the actual distance between the elemental mass and the reference axis should be used. The moments of inertia about axes x and z, can be determined by parallel-axis theorem. Imply

image

And the moments of inertia about axis y can also be determined by parallel-axis theorem. Imply

image

Moment of Inertia of Circular Cone

image

Consider a homogenous circular cone of height h with base area A of radius r and homogenouse material density l. The material density is a constant, the mass and the elemental mass of the circular cone can be expressed in terms of the volume of the circular cone. Since the radius r of the base area cannot be neglected, the actual distance between the elemental mass and the reference axis should be used. The moments of inertia about axes x and z, can be determined by parallel-axis theorem. Imply

image

And the moments of inertia about axis y can also be determined by parallel-axis theorem. Imply

image

Moment of Inertia of Sphere

image

Consider a homogenous sphere of radius r and homogenouse material density l. The material density is a constant, the mass and the elemental mass of the circular cone can be expressed in terms of the volume of the circular cone. Since the radius r of the sphere area cannot be neglected, the actual distance between the elemental mass and the reference axis should be used. The moments of inertia about axes x, y and z, can be determined by triple integration. Imply

image

©sideway

ID: 121100086 Last Updated: 14/11/2012 Revision: 0 Ref:

close

References

  1. F.P. Beer; E.R. Johnston,Jr.; E.R. Eisenberg, 2004, Vector Mechanics for Engineers: Statics
  2. I.C. Jong; B.G. rogers, 1991, Engineering Mechanics: Statics and Dynamics
close

Latest Updated LinksValid XHTML 1.0 Transitional Valid CSS!Nu Html Checker Firefox53 Chromena IExplorerna
IMAGE

Home 5

Business

Management

HBR 3

Information

Recreation

Hobbies 8

Culture

Chinese 1097

English 337

Reference 67

Computer

Hardware 151

Software

Application 202

Digitization 25

Latex 9

Manim 123

Numeric 19

Programming

Web 285

Unicode 494

HTML 65

CSS 59

ASP.NET 194

OS 391

DeskTop 7

Python 23

Knowledge

Mathematics

Formulas 8

Algebra 29

Number Theory 206

Trigonometry 18

Geometry 21

Calculus 67

Complex Analysis 21

Engineering

Tables 8

Mechanical

Mechanics 1

Rigid Bodies

Statics 92

Dynamics 37

Fluid 5

Fluid Kinematics 5

Control

Process Control 1

Acoustics 19

FiniteElement 2

Physics

Electric 27

Biology 1

Geography 1


Copyright © 2000-2020 Sideway . All rights reserved Disclaimers last modified on 06 September 2019