Moment of Inertia II: 3D Shapes

Name Picture Dimensions Defining Equation Principal Moments about O
Ix Iy Iz
Solid
Cuboid
sides:
2a, 2b, 2c
-a < x < a
-b < y < b
-c < z < c
1/3M(b2+c2) 1/3M(c2+a2) 1/3M(a2+b2)
Solid
Cylinder
radius, a
height, 2h
x2 + y2 < a2
-h < z < h
1/4Ma2 + 1/3Mh2 1/2Ma2
Solid
Cone
radius, a
height, 2h
x2 + y2 < (az/h)2
0 < z < h
3/20Ma2 + 3/5Mh2 3/10Ma2
Solid
Sphere
radius, a x2 + y2 + z2 < a2 2/5Ma2
Spherical
Shell
radius, a x2 + y2 + z2 = a2 2/3Ma2