Moment of Inertia I: Simple Laminae

Name Picture Dimensions Defining Equation Principal Moments about O
Ix Iy Iz
Uniform
Rod
length, 2a x = y = 0
-a < z < a
1/3Ma2 0
Circular
Rim
radius, a x2 + y2 = a2
z = 0
1/2Ma2 Ma2
Circular
Disk
radius, a x2 + y2 < a2
z = 0
1/4Ma2 1/2Ma2
Rectangular
Lamina
width, 2a
length, 2b
-a < x < a
-b < y < b
z = 0
1/3Mb2 1/3Ma2 1/3M(a2+b2)
Elliptical
Disk
principal
semi-axes,
a and b
(x/a)2 + (y/b)2 < 1
z = 0
1/4Mb2 1/4Ma2 1/4M(a2+b2)
Annulus radii, b < a b2 < x2 + y2 < a2
z = 0
1/4M(a2+b2) 1/2M(a2+b2)