# Unit of moment of inertia

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1. Jul 21, 2015

### lingesh

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?

2. Jul 21, 2015

### Orodruin

Staff Emeritus
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.

3. Jul 21, 2015

### SteamKing

Staff Emeritus
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

4. Jul 21, 2015

Thanks...