From: ted@rosencrantz.stcloudstate.edu
Subject: Re: calculation of angular acceleration of a rigid body
Date: Fri, 11 Aug 2000 04:29:31 GMT
Newsgroups: sci.physics.research
Summary: [missing]

In article <398d4f1a.3683159@news.uta1002.at>,
Christoph Nocker <christoph.nocker@gmx.net> wrote:

>But how can I get the angular acceleration?
>The formula should look like this then:
>angular acceleration = torque / moment of inertia
>
>But how can I divide a 3d vector with an other 3d vector?

The moment of inertia is not actually a vector; it's a rank-2 tensor.
You can represent it as a 3x3 symmetric matrix, and then the equation

torque = (moment of inertia) (angular acceleration)

makes sense: 3-vector = 3x3 matrix times 3-vector.

You can always set up your x,y,z axes in such a way that that
matrix is diagonal, so that you only have to calculate 3 numbers
to work out the moment of inertia.  These axes are called the principal
axes of the object, and if the object is reasonably symmetric then
you can typically guess how they're oriented.  If your axes
are oriented this way, then the above equation works component
by component:

torque_x = (moment of inertia)_x (angular acceleration)_x

and the same for y and z.  But if your axes aren't aligned
with the objects principal axes, that won't be true.

-Ted