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Table of moments of inertia

Source:
The Concise Oxford Dictionary of Mathematics

Appendix 3. Table of moments of inertia

For uniform bodies of mass M.

Thin rod, length 2l, about perpendicular axis through centre:

Ml 2.

Rectagular lamina, about axis in plane bisecting edges of length 2l:

Ml 2.

Thin rod, length 2l, about perpendicular axis through end:

4/3 Ml 2.

Rectagular lamina, about edge perpendicular to edges of length 2l:

4/3 Ml 2.

Rectagular lamina, sides 2 l and 2 b , about perpendicular axis through centre:

M(l 2 + b 2).

Hoop or cylindrical shell, radius r , about axis;

Mr 2

Hoop, radius r, about a diameter;

½Mr 2

Disc or solid cylinder, radius r , about axis;

½Mr 2

Disc, radius r, about a diameter;

¼Mr 2

Solid sphere, radius r , about a diameter:

2/5 Mr 2

Spherical shell, radius r , about a diameter:

Mr 2

Elliptical lamina, axes 2 a and 2 b , about axis of length 2 a :

¼Mb 2.

Elliptical lamina, axes 2 a and 2 b , about perpendicular axis through centre:

¼M(a 2 + b 2).

Solid ellipsoid, axes 2 a , 2 b and 2 c , about axis of length 2 c :

1/5 M(a 2 + b 2).

Ellipsoidal shell, axes 2 a , 2 b and 2 c , about axis of length 2 c :

M(a 2 + b 2).

Right circular cone, base radius r , about axis of cone:

3/10 Mr 2.