list of moments of inertia

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9/29/13 List of moments of inertia - Wikipedia, the free encyclopedia

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List of moments of inertiaFrom Wikipedia, the free encyclopedia

The mass moment of inertia, usually denotedI, measures the extent to which an object resists rotational acceleration about an axis, and is the rotational analogue to mass. Mass mof inertia have units of dimension mass length2. It should not be confused with the second moment of area, which is used in bending calculations.

Geometrically simple objects have moments of inertia that can be expressed mathematically, but it may not be straightforward to symbolically express the moment of inertia of mo

complex bodies.

The following moments of inertia assume constant density throughout the object, and the axis of rotation is taken to be through the centre of mass, unless otherwise specified.

Moments of inertiaDescription Figure Moment(s) of inertia

Point mass mat a distancerfrom the axis

of rotation.

A point m

axis, but b

around a d

Two point masses,Mand m, with

reduced mass and separated by a

distance,x.

Rod of lengthLand mass m

(Axis of rotation at the end ofthe rod) [1]

This expre

wire. This

axis of rot

Rod of lengthLand mass m [1]

This expre

wire. This

of rotation

Thin circular hoop of radius rand mass m

This is a s

as of a thi

and h= 0

Thin, solid disk of radius rand mass m

This is a s

theorem.

Thin cylindrical shell with open ends, of

radius rand mass m [1]

This expre

special ca

Also, a po

same mom

gyration.

Solid cylinder of radius r, height hand

mass m

[1] This is a s

= 0. (Note

handed fr

Thick-walled cylindrical tube with open

ends, of inner radius r1, outer radius r2,

[1][2]

With a den
http://en.wikipedia.org/wiki/File:Moment_of_inertia_solid_cylinder.svghttp://en.wikipedia.org/wiki/File:Moment_of_inertia_solid_cylinder.svghttp://en.wikipedia.org/wiki/File:Moment_of_inertia_thin_cylinder.pnghttp://en.wikipedia.org/wiki/File:Moment_of_inertia_thin_cylinder.pnghttp://en.wikipedia.org/wiki/File:Moment_of_inertia_disc.svghttp://en.wikipedia.org/wiki/File:Moment_of_inertia_disc.svghttp://en.wikipedia.org/wiki/File:Moment_of_inertia_disc.svghttp://en.wikipedia.org/wiki/File:Moment_of_inertia_hoop.svghttp://en.wikipedia.org/wiki/File:Moment_of_inertia_hoop.svghttp://en.wikipedia.org/wiki/File:Moment_of_inertia_rod_center.svghttp://en.wikipedia.org/wiki/File:Moment_of_inertia_rod_center.svghttp://en.wikipedia.org/wiki/File:Moment_of_inertia_rod_end.svghttp://en.wikipedia.org/wiki/File:Moment_of_inertia_solid_cylinder.svghttp://en.wikipedia.org/wiki/Radius_of_gyrationhttp://en.wikipedia.org/wiki/File:Moment_of_inertia_thin_cylinder.pnghttp://en.wikipedia.org/wiki/Cylinder_(geometry)http://en.wikipedia.org/wiki/Perpendicular_axis_theoremhttp://en.wikipedia.org/wiki/File:Moment_of_inertia_disc.svghttp://en.wikipedia.org/wiki/Disk_(mathematics)http://en.wikipedia.org/wiki/File:Moment_of_inertia_hoop.svghttp://en.wikipedia.org/wiki/Hoophttp://en.wikipedia.org/wiki/File:Moment_of_inertia_rod_center.svghttp://en.wikipedia.org/wiki/Rod_(geometry)http://en.wikipedia.org/wiki/File:Moment_of_inertia_rod_end.svghttp://en.wikipedia.org/wiki/Rod_(geometry)http://en.wikipedia.org/wiki/Reduced_masshttp://en.wikipedia.org/wiki/Second_moment_of_areahttp://en.wikipedia.org/wiki/Physical_unithttp://en.wikipedia.org/wiki/Moment_of_inertia


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length hand mass m or when defining the normalized thickness tn= t/rand letting r= r2,

then

Tetrahedron of sidesand mass m

Octahedron (hollow) of sidesand mass

m

Octahedron (solid) of sidesand mass m

Sphere (hollow) of radius rand mass m [1]

A hollow

infinitesim

to r(or a

Ball (solid) of radius rand mass m [1]

A sphere

infinitesim

(or a sing

Also, it ca

spheres, w

Sphere (shell) of radius r2, with centered

spherical cavity of radius r1and mass m [1]

When the

When r1=

hollow sp

Right circular cone with radius r, height h

and mass m

[3]

[3]
http://en.wikipedia.org/wiki/File:Moment_of_inertia_cone.svghttp://en.wikipedia.org/wiki/Cone_(geometry)http://en.wikipedia.org/wiki/Right_anglehttp://en.wikipedia.org/wiki/File:Spherical_shell_moment_of_inertia.pnghttp://en.wikipedia.org/wiki/Spherehttp://en.wikipedia.org/wiki/File:Moment_of_inertia_solid_sphere.svghttp://en.wikipedia.org/wiki/Ball_(mathematics)http://en.wikipedia.org/wiki/File:Moment_of_inertia_hollow_sphere.svghttp://en.wikipedia.org/wiki/Spherehttp://en.wikipedia.org/wiki/File:Octahedral_axis.gifhttp://en.wikipedia.org/wiki/Octahedronhttp://en.wikipedia.org/wiki/File:Octahedral_axis.gifhttp://en.wikipedia.org/wiki/Octahedronhttp://en.wikipedia.org/wiki/File:Tetraaxial.gifhttp://en.wikipedia.org/wiki/Tetrahedronhttp://en.wikipedia.org/wiki/File:Moment_of_inertia_thick_cylinder_h.svg


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Torus of tube radius a, cross-sectional

radius band mass m.

About a diameter: [4]

About the vertical axis: [4]

Ellipsoid (solid) of semiaxes a, b, and c

with axis of rotation aand mass m

Thin rectangular plate of height hand of

width wand mass m

(Axis of rotation at the end of the plate)

Thin rectangular plate of height hand of

width wand mass m [1]

Solid cuboid of height h, width w, and

depth d, and mass m

For a simi

Solid cuboid of heightD, width W, and

lengthL, and mass mwith the longest

diagonal as the axis.

For a cub

Plane polygon with vertices , , ,

..., and

mass uniformly distributed on its

interior, rotating about an axis

perpendicular to the plane and passing

through the origin.

This expre

vectors

Infinite disk with mass normally
http://en.wikipedia.org/wiki/Normally_distributedhttp://en.wikipedia.org/wiki/Normally_distributedhttp://en.wikipedia.org/wiki/Disk_(mathematics)http://en.wikipedia.org/wiki/File:Polygon_moment_of_inertia.pnghttp://en.wikipedia.org/wiki/Polygonhttp://en.wikipedia.org/wiki/File:Moment_of_Inertia_Cuboid.svghttp://en.wikipedia.org/wiki/Cuboidhttp://en.wikipedia.org/wiki/File:Moment_of_inertia_solid_rectangular_prism.pnghttp://en.wikipedia.org/wiki/Cuboidhttp://en.wikipedia.org/wiki/File:Recplane.svghttp://en.wikipedia.org/wiki/File:Recplaneoff.svghttp://en.wikipedia.org/wiki/File:Ellipsoid_321.pnghttp://en.wikipedia.org/wiki/Ellipsoidhttp://en.wikipedia.org/wiki/File:Torus_cycles.pnghttp://en.wikipedia.org/wiki/Torus


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distributed on two axes around the axis of

rotation

(i.e.

Where : is the mass-density as a

functionof x and y).

See also

Moment of inertia

Parallel axis theorem

Perpendicular axis theorem

List of area moments of inertia

List of moment of inertia tensors

References

1. ^ abcdefghiRaymond A. Serway (1986).Physics for Scientists and Engineers, second ed. Saunders College Publishing. p. 202. ISBN 0-03-004534-7.

2. ^Classical Mechanics - Moment of inertia of a uniform hollow cylinder (http://www .livephysics.c om/problems-and-answers /classical-mechanics/find-moment-of-inertia-of-a-unifo

hollow-cylinder.html). LivePhysics.com. Retrieved on 2008-01-31.

3. ^ abFerdinand P. Beer and E. Russell Johnston, Jr (1984). Vector Mechanics for Engineers, fourth ed. McGraw-Hill. p. 911. ISBN 0-07-004389-2.

4. ^ abEric W. Weisstein. "Moment of Inertia Ring" (http://scienceworld.wolfram.com/physics/MomentofInertiaRing.html). Wolfram Research. Retrieved 2010-03-25.

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