Polar Moment of Inertia Machinery's Handbook, 31st Edition
253
Formulas for Polar Moment of Inertia of Masses, J M
Prism:
A
A
l l
B
B
With reference to axis AA : J M h b 12 M 2 2 = + ^ h With reference to axis BB : J M l h 3 12 M 2 2 = + a k
A
A
A
h
B
B
h
b
b
Cylinder: A
A
l l
Mr 2 1
B
B
2
With reference to axis AA : J
=
M
A
A
With reference to axis BB : J M l r 3 4 M 2 2 = + a k
A
B
B
r
r
Hollow Cylinder:
A
l l
M R r 2 1 2 2 + ^ h
B
B
With reference to axis AA : J With reference to axis BB : J M l 2
=
M
A
R r 2 2 = + + a k
R
r
4
3
r
B
B
M
A
R
Pyramid, Rectangular Base:
A
With reference to axis AA : J M a b 20 M 2 2 = + ^ h With reference to axis BB (through the center of gravity): J M h b 80 3 20 M 2 2 = + a k
h
B
B
A
A
b
b
B
B
a
a
Sphere:
r
With reference to any axis through the center: J Mr 5 2 M 2 =
A
A
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