# Moment of Inertia, Strong/Weak axis?

1. Oct 14, 2008

### subwaybusker

Hello, can anyone explain to me what the moment of inertia is? we learnt the mass moment, second moment and the first, and i'm getting confused as to what they all are. and can anyone explain what the strong/weak axis is? is it resistance to bending or rotation? i just can't visualize where the strong/weak axis would be on a ruler and our prof drew x and y axes but they don't make sense to me unless...you tilt the ruler?

he drew something like with the width of the ruler (not thickness) along the y axis.

y
|
---------------|------------x
|

2. Oct 14, 2008

### minger

Yea, they can be quite confusing and when doing a calculationg it's important to check your units to make sure that you're calculating the proper moment of inertia. With that in mind, here are some of them:

Mass Moment of Inertia - Resists angular acceleration. Analogous to mass and linear acceleration:
units: $$kg \cdot m^2$$
Used in the Equation $$T = I\omega$$

Area Moment of Inertia (second moment) - Resists Bending
units: $$m^4$$
Used in the Stress Calculations like $$\sigma = \frac{Mc}{I}$$

Polar Moment of Inertia - Resists Torsion
units: $$m^4$$
Used in the Equation $$\tau = \frac{Tr}{J}$$

In my experience, Polar Moment of Inertia and Area Moment of inertia get confused along the axis of a shaft or other long part; they are not the same thing. It can be shown that the polar moment of inertia is the sum of the other two off axis moments of inertia. If the x-axis runs along a shaft, then $$J = I_{yy} +I_{zz}}$$

Last edited: Oct 14, 2008