What is the relationship between rotational inertia and the inertia tensor?

[chrisyuen]

Homework Statement

What is moment of inertia?

Homework Equations

N/A

The Attempt at a Solution

Some people said that it is not a scalar and also not a vector.

But other said that if it is not a vector, it must be a scalar.

However, another said that it is actually a tensor.

Can anyone tell me what it is?

 

[PalashD]

It is a tensor. Check wikipedia for details
http://en.wikipedia.org/wiki/Moment_of_inertia

 

[Dr.D]

For a mass distribution, there is a tensor quantity called the mass moment of inertia tensor.

In rigid body dynamics problems, in 3D, the full inertia tensor is significant. In 2D, the quantity that is significant for the rotational inertia is related to the inertia tensor as
Is = (n) {n}
where
Is = scalar effective mass MOI
(n) = row form for unit vector along the axis of rotation
{n} = column fomr for unit vector along the axis of rotation
= mass MOI matrix (2nd order tensor)