List of moments of inertia
1
List of moments of inertia
Description Figure Moment(s) of inertia Comment
Point mass m at a distance r from the axis A point mass does not have a moment of inertia around
of rotation. axis, but by using the parallel axis theorem a moment of
around a distant axis of rotation is achieved.
Two point masses, M and m, with reduced 
mass and separated by a distance, x.
Rod of length L and mass m This expression assumes that the rod is an infinitely thin
[1]
(Axis of rotation at the end of the rod) rigid) wire. This is also a special case of the thin rectang
with axis of rotation at the end of the plate, with h = L a
Rod of length L and mass m This expression assumes that the rod is an infinitely thin
[1]
rigid) wire. This is a special case of the thin rectangular
axis of rotation at the center of the plate, with w = L and
Thin circular hoop of radius r and mass m This is a special case of a torus for b=0. (See below.), as
a thick-walled cylindrical tube with open ends, with r1=
h=0.
Thin, solid disk of radius r and mass m This is a special case of the solid cylinder, with h=0.
Thin cylindrical shell with open ends, of [1] This expression assumes the shell thickness is negligibl
radius r and mass m special case of the thick-walled cylindrical tube for r1=r
point mass (m) at the end of a rod of length r has this sa
moment of inertia and the value r is called the radius of
Solid cylinder of radius r, height h and This is a special case of the thick-walled cylindrical tub
[1]
mass m r1=0. (Note: X-Y axis should be swapped for a standard
handed frame)
Thick-walled cylindrical tube with open With a density of Á and the same geometry
[1][2]
ends, of inner radius r1, outer radius r2,
length h and mass m
or when defining the normalized thickness tn = t/r and letting r = r2,
then
Sphere (hollow) of radius r and mass m A hollow sphere can be taken to be made up of two stac
[1]
infinitesimally thin, circular hoops, where the radius dif
0 to r (or a single stack, , where the radius differs from -
Ball (solid) of radius r and mass m A sphere can be taken to be made up of two stacks of
[1]
infinitesimally thin, solid discs, where the radius differs
r (or a single stack, where the radius differs from -r to r
can be taken to be made up of infinitesimally thin, hollo
where the radius differs from 0 to r.
List of moments of inertia
2
Right circular cone with radius r, height h 
[3]
and mass m
[3]
Torus of tube radius a, cross-sectional 
[4]
About a diameter:
radius b and mass m.
[4]
About the vertical axis:
Ellipsoid (solid) of semiaxes a, b, and c 
with axis of rotation a and mass m
Thin rectangular plate of height h and of 
width w and mass m
(Axis of rotation at the end of the plate)
Thin rectangular plate of height h and of 
[1]
width w and mass m
Solid cuboid of height h, width w, and For a similarly oriented cube with sides of length ,
depth d, and mass m
.
Solid cuboid of height D, width W, and
For a cube with sides , .
length L, and mass m with the longest
diagonal as the axis.
This expression assumes that the polygon is star-shaped
Plane polygon with vertices , ,
vectors , , , ..., are position vectors of th
, ..., and mass uniformly
vertices.
distributed on its interior, rotating about an
axis perpendicular to the plane and passing
through the origin.
Infinite disk with mass normally 
distributed on two axes around the axis of
rotation (i.e.
Where : is the mass-density as a
function of x and y).
List of moments of inertia
3
References
[1] Raymond 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. com/ problems-and-answers/
classical-mechanics/ find-moment-of-inertia-of-a-uniform-hollow-cylinder. html). LivePhysics.com. Retrieved on 2008-01-31.
[3] Ferdinand P. Beer and E. Russell Johnston, Jr (1984). Vector Mechanics for Engineers, fourth ed.. McGraw-Hill. p. 911.
ISBN 0-07-004389-2.
[4] Eric W. Weisstein. "Moment of Inertia  Ring" (http:/ / scienceworld. wolfram. com/ physics/ MomentofInertiaRing. html). Wolfram
Research. . Retrieved 2010-03-25.
Article Sources and Contributors
4
Article Sources and Contributors
List of moments of inertia Source: http://en.wikipedia.org/w/index.php?oldid=521803613 Contributors: 11kravitzn, A. di M., A19grey, Annom, AquaDTRS, ArnoldReinhold, Ave matthew,
Baccyak4H, Bearasauras, Biscuittin, Bochum, Centrx, CiaPan, Copsi, CosineKitty, Ctrl build, Da Joe, Dexter411, Dger, Dinglebarf, Dudecon, Email4mobile, Ems57fcva, Fresheneesz, Gerweck,
Giftlite, Glome83, Grendelkhan, Hammerite, Hanavi, Headbomb, Hemmingsen, Herbee, Icairns, Icemaja, InverseHypercube, J-Wiki, JForget, Jeffcanfly, Joerger, Johnmc67, Just James,
KasugaHuang, Kevin B12, Kolkje, Krishnavedala, LPFR, Laurascudder, Masrudin, Mikiemike, Minesweeper, NOrbeck, Nick Number, Obiliz, Paste, Patrick, Pearlsawmeismyname, Prince Max
(scientist), Pt, Qef, Ram einstein, RedWolf, Scientific29, Segv11, Sonett72, Starwiz, Stpasha, Tagishsimon, TimBentley, Tresiden, Truthnlove, Zigger, 169 anonymous edits
Image Sources, Licenses and Contributors
Image:moment of inertia rod end.svg Source: http://en.wikipedia.org/w/index.php?title=File:Moment_of_inertia_rod_end.svg License: Creative Commons Zero Contributors:
User:Krishnavedala
Image:moment of inertia rod center.svg Source: http://en.wikipedia.org/w/index.php?title=File:Moment_of_inertia_rod_center.svg License: Creative Commons Zero Contributors:
User:Krishnavedala
Image:moment of inertia hoop.svg Source: http://en.wikipedia.org/w/index.php?title=File:Moment_of_inertia_hoop.svg License: GNU Free Documentation License Contributors: Original
MetaPost program by en:User:Grendelkhan Program tweaked adjust axes labels to match bitmap version and to avoid negative coordinates in PostScript output and rendered as SVG by Qef
Image:moment of inertia disc.svg Source: http://en.wikipedia.org/w/index.php?title=File:Moment_of_inertia_disc.svg License: GNU Free Documentation License Contributors: Original
MetaPost program by en:User:Grendelkhan Program tweaked adjust axes labels and fill in the grey disc to match bitmap version and to avoid negative coordinates in PostScript output and
rendered as SVG by Qef
Image:moment of inertia thin cylinder.png Source: http://en.wikipedia.org/w/index.php?title=File:Moment_of_inertia_thin_cylinder.png License: Public Domain Contributors:
http://www.vectorsite.net/gfxzmain.html
Image:moment of inertia solid cylinder.svg Source: http://en.wikipedia.org/w/index.php?title=File:Moment_of_inertia_solid_cylinder.svg License: GNU Free Documentation License
Contributors: Original MetaPost program by en:User:Grendelkhan Program tweaked to avoid negative coordinates in PostScript output and rendered as SVG by Qef
Image:moment of inertia thick cylinder h.svg Source: http://en.wikipedia.org/w/index.php?title=File:Moment_of_inertia_thick_cylinder_h.svg License: Creative Commons Zero
Contributors: User:Krishnavedala
Image:moment of inertia hollow sphere.svg Source: http://en.wikipedia.org/w/index.php?title=File:Moment_of_inertia_hollow_sphere.svg License: GNU Free Documentation License
Contributors: Original MetaPost program by en:User:Grendelkhan Program tweaked adjust axes labels to match bitmap version and to avoid negative coordinates in PostScript output and
rendered as SVG by Qef
Image:moment of inertia solid sphere.svg Source: http://en.wikipedia.org/w/index.php?title=File:Moment_of_inertia_solid_sphere.svg License: GNU Free Documentation License
Contributors: Original MetaPost program by en:User:Grendelkhan Program tweaked adjust axes labels and fill in the grey circle to match bitmap version and to avoid negative coordinates in
PostScript output and rendered as SVG by Qef
Image:moment of inertia cone.svg Source: http://en.wikipedia.org/w/index.php?title=File:Moment_of_inertia_cone.svg License: GNU Free Documentation License Contributors: Original
MetaPost program by en:User:Grendelkhan Program tweaked to avoid negative coordinates in PostScript output and rendered as SVG by Qef Manually edited in inkscape to fixing intersection by
Wiso
Image:torus cycles.png Source: http://en.wikipedia.org/w/index.php?title=File:Torus_cycles.png License: GNU Free Documentation License Contributors: User:Fropuff
Image:Ellipsoid 321.png Source: http://en.wikipedia.org/w/index.php?title=File:Ellipsoid_321.png License: Public domain Contributors: Thrawn562 at en.wikipedia
Image:Recplaneoff.svg Source: http://en.wikipedia.org/w/index.php?title=File:Recplaneoff.svg License: Public Domain Contributors: User:Reubot
Image:Recplane.svg Source: http://en.wikipedia.org/w/index.php?title=File:Recplane.svg License: Public Domain Contributors: User:Reubot
Image:moment of inertia solid rectangular prism.png Source: http://en.wikipedia.org/w/index.php?title=File:Moment_of_inertia_solid_rectangular_prism.png License: Public Domain
Contributors: http://www.vectorsite.net/gfxzmain.html
Image:Moment of Inertia Cuboid.svg Source: http://en.wikipedia.org/w/index.php?title=File:Moment_of_Inertia_Cuboid.svg License: Creative Commons Zero Contributors:
User:Krishnavedala
Image:Polygon moment of inertia.png Source: http://en.wikipedia.org/w/index.php?title=File:Polygon_moment_of_inertia.png License: Public Domain Contributors: Glome83
File:Gaussian 2D.png Source: http://en.wikipedia.org/w/index.php?title=File:Gaussian_2D.png License: Public Domain Contributors: User:Michael Hardy
License
Creative Commons Attribution-Share Alike 3.0 Unported
//creativecommons.org/licenses/by-sa/3.0/