# Inertia tensor

1. Feb 20, 2008

### ehrenfest

1. The problem statement, all variables and given/known data
What is the relationship between the inertia tensor and the rotational inertia? How can a second-rank tensor describe the same thing as a scalar? Is their a formula to go between one and the other i.e. if I have an inertia tensor for a rigid body rotating about some axis, can I get the rational inertia of the body about that axis from that?

EDIT: I see. Please notice that the inertia tensor IS DEFINED WITH RESPECT TO A COORDINATE SYSTEM while a moment of inertia IS DEFINED WITH RESPECT TO AN AXIS. In fact, the inertia tensor contains the information about the rotational inertias about the 3 axes of the coordinate with respect to which it is defined. These are simply the diagonals. Please confirm this.
EDIT EDIT: If I have an inertia tensor with respect to a coordinate system with axes $$\hat{i},\hat{j},\hat{k}$$, how do you get the moment of inertia about an axis that is not equal to one of $$\hat{i},\hat{j},\hat{k}$$?
2. Relevant equations

3. The attempt at a solution

Last edited: Feb 20, 2008
2. Feb 20, 2008

### Mindscrape

Are you asking about is how to diagonalize the inertia tensor to use principle axes or asking about Steiner's parallel axis theorem?