Why Are There Different Units for Moment of Inertia?

AI Thread Summary
The discussion clarifies the confusion surrounding the different units for moment of inertia (MI). The area moment of inertia, used for bending stress calculations, has units of length to the fourth power (L^4), while the mass moment of inertia (MMOI) has units of mass times length squared (M L^2). The formula for the area moment of inertia of a rectangle is b*d^3/12, assuming a surface density of one. In contrast, the MMOI relates torque to angular acceleration, analogous to F = ma in linear motion. Understanding these distinctions is crucial for applying the correct concepts in engineering and physics.
lingesh
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Hi,
I am a bit confused about the units of MI...I read that MI of rectangle is b*d^3/12,so unit is mm^4..Also i read in wiki that unit of MI is kg.mm^2...

Both are correct,but why this difference is?
 
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The correct dimension is mass x length^2. The expression for the rectangle you found assumes a surface density of one and the actual expression should be multiplied by the surface density, which will also result in a dimension of mass x length^2.
 
lingesh said:
Hi,
I am a bit confused about the units of MI...I read that MI of rectangle is b*d^3/12,so unit is mm^4..Also i read in wiki that unit of MI is kg.mm^2...

Both are correct,but why this difference is?

You are getting two different moments of inertia confused.

The area moment of inertia, sometimes called the second moment of area, has units of L4. The second moment of area of a rectangle is bd3/12, when referenced to the centroid of the rectangle. The area moment of inertia is chiefly used to determine things like bending stresses in beams.

https://en.wikipedia.org/wiki/Second_moment_of_area

The mass moment of inertia, sometimes abbreviated MOI or MMOI, is a slightly different concept. The MMOI has units of M L2.

The MMOI relates the torque applied to a body to its angular acceleration, T = I α, and is analogous to F = ma for rectilinear motion.

https://en.wikipedia.org/wiki/Moment_of_inertia
 
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SteamKing said:
You are getting two different moments of inertia confused.

The area moment of inertia, sometimes called the second moment of area, has units of L4. The second moment of area of a rectangle is bd3/12, when referenced to the centroid of the rectangle. The area moment of inertia is chiefly used to determine things like bending stresses in beams.

https://en.wikipedia.org/wiki/Second_moment_of_area

The mass moment of inertia, sometimes abbreviated MOI or MMOI, is a slightly different concept. The MMOI has units of M L2.

The MMOI relates the torque applied to a body to its angular acceleration, T = I α, and is analogous to F = ma for rectilinear motion.

https://en.wikipedia.org/wiki/Moment_of_inertia
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