Moment of Inertia Formula sheet |the Moment of Inertia formula for all basic structures| Mechanics|
23 Jan 2017
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Shape of the body
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Axis Of rotation
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Expression for Moment of
Inertia
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One dimensional rod
of mass M and length
L
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1) Center of Rod and ┴ to length
2) One end
and ┴ to length
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ML2
12
ML2
3
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Sphere of mass M and
Radius
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1) Any diameter
2) Any tangent plane
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(2 / 5)MR 2
(7 / 5)MR 2
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Circular disc of Mass
and radius R
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1) Through center, ┴ to plane of
Disk
2) any diameter
3) tangent in the plane of
the disc
4) tangent ┴ to plane of
disk
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(1/ 2)MR 2 (1/ 4)MR 2 (5
/ 4)MR 2 (3
/ 2)MR 2
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Circular ring of mass
M and radius R
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1) Through center, ┴ to plane of
ring
2) any diameter
3) tangent in the plane of
the ring
4) tangent ┴ to plane of
ring
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MR 2
(1/ 2)MR 2
(3 / 2)MR 2
2MR 2
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Cylinder of mass
M ,radius R and length
L
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1) own axis
2) through center ┴ to length
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(1/ 2)MR 2
R 2 L2
M ( +
)
4 12
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Rectangular lamina of
Mass M,length L and breath B
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1) Length of lamina and in its
plane
2) breath of lamina and in its plane
3) Center of lamina and ┴
to its plane
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MB 2
3
ML2
3
M (L2 + B 2 )
12
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Rectangular block of
Mass M,Length L,Breadth B and Height H
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Through center of block and
parallel to Length or breadth or height of the block
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M (H 2 + B 2 )
12
M (L + H 2 )
12
M (L2 + B 2 )
12
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