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Table of Selected Moments of Inertia
Point mass at a radius R
Thin rod about axis through
center perpendicular to length
‫=ܫ‬
‫ ܴܯ = ܫ‬ଶ
Thin-walled cylinder about
central axis
‫ ܴܯ = ܫ‬ଶ
Solid cylinder about central
diameter
1
‫ ܴܯ = ܫ‬ଶ
2
1
‫ܮܯ‬ଶ
12
Thick-walled cylinder about
central axis
1
‫ܮܯ = ܫ‬ଶ
3
Solid cylinder about central axis
1
‫ ܴܯ = ܫ‬ଶ
2
1
‫ܯ = ܫ‬ሺܴଵଶ + ܴଶଶ ሻ
2
Solid sphere about center
1
1
‫ ܴܯ = ܫ‬ଶ + ‫ܮܯ‬ଶ
4
12
Thin ring about diameter
Thin rod about axis through end
perpendicular to length
Thin hollow sphere about center
2
‫ ܴܯ = ܫ‬ଶ
5
Slab about perpendicular axis
through center
‫=ܫ‬
2
‫ ܴܯ = ܫ‬ଶ
3
Cone about central axis
1
‫ܯ‬ሺܽଶ + ܾ ଶ ሻ
12
Note: All formulas shown assume objects of uniform mass density.
‫=ܫ‬
3
‫ ܴܯ‬ଶ
10