# First year Applied maths question on Inertia Perpendicular Axes Theorem

• Mar 13th 2011, 12:41 AM
iva
First year Applied maths question on Inertia Perpendicular Axes Theorem
Hi everyone, hope this is the right forum to put this question.

I've just read the theorem in my study guide called: Perpendicular Axes Theorem

It says that if X, Y and Z are mutually perpendicular axes of rotation, and assuming a rigid body forms a lamina which likes on the XY-plane then

Iz = Ix + Iy (I being moments of inertia about each respective axes)

It looks so simple BUT not every situation is it clear what axes is X, Y, or Z, so say you have 2 out of 3, how do you know that those 2 are the Z and X axes and you need to then subtract rather than add values. Is it always going to be obvious? Is there a way to know?

Thanks!
• Mar 13th 2011, 09:36 AM
topsquark
Quote:

Originally Posted by iva
Hi everyone, hope this is the right forum to put this question.

I've just read the theorem in my study guide called: Perpendicular Axes Theorem

It says that if X, Y and Z are mutually perpendicular axes of rotation, and assuming a rigid body forms a lamina which likes on the XY-plane then

Iz = Ix + Iy (I being moments of inertia about each respective axes)

It looks so simple BUT not every situation is it clear what axes is X, Y, or Z, so say you have 2 out of 3, how do you know that those 2 are the Z and X axes and you need to then subtract rather than add values. Is it always going to be obvious? Is there a way to know?

Thanks!

Typically the only use of this theorem is when there are symmetries. For example, you can easily calculate the moment of inertia for a rod along the axis down the center of the rod. So you can then calculate the moment of inertia in the direction perpendicular to this. For situations where there is no symmetry to work with you would probably have to resort to numerical calculation in which point you would calcuate the moment of inertia directly without reference to an axis you could calculate it from.

-Dan