Principal Mass Moments of Inertia of Solid Geometrical Shapes

Ix Iy Iz

Slender Rod 0 1/12 ml2 1/12 ml2

m = mass, l = length of rod

Rectangular Plate 1/12 m(b2+c2) 1/12 mc2 1/12 mb2

m = mass, b = height of plate, c = width of plate

Thin Disk ½ mr2 ¼ mr2 ¼ mr2

m = mass, r = radius of disk

Rectangular Prism 1/12 m(b2+c2) 1/12 m(a2+c2) 1/12 m(a2+b2)m = mass, a = depth (x), b = height (y), c = width (z)

Circular Cylinder ½ mr2 1/12 m(3r2+l2) 1/12 m(3r2+l2)m = mass, l = length of cylinder, r = radius

Elliptical Cylinder ¼ m(b2 +c2) 1/12 m(3c2

+l2) 1/12 m(3b2 +l2)

m = mass, l = length of cylinder (x), b = height/2 (y), c = width/2 (z)

Circular Cone 3/10 mr2 3/5 m(¼ r2 + l2) 3/5 m(¼ r2 + l2)m = mass, l = length of cone, r = radius at base

Sphere 2/5 mr2 2/5 mr2 2/5 mr2

m = mass, r = radius

Ellipsoid 1/5 m(b2+c2) 1/5 m(a2+c2) 1/5 m(a2+b2)m = mass, a = depth (x), b = height (y), c = width (z)