Engr210 – Spring 2005
Lesson # 35: Product of Inertia
Today’s Objective:
a) Determine product of inertia of
an area
Instructor: Ahmed Abdel-Rahim
Page 1 of 2
Product of Inertia for an area
Product of Inertia for an area
Moment of Inertia for an area is
different for every axis
Sometimes, we need to find the
orientation of axes which gives Imax
Similar to Ix and Iy:
Imax depends on Ix, Iy and Ixy [product of
Inertia]
General Rule:
If either x or y axis is an axis of
symmetry for the area THEN Ixy =0
Product of inertia of Composite areas
Using the parallel-axis theorem, the
Product of Inertia for a composite area can
easily be calculated.
For right angle triangles: Ixy=b2h2/8
I xy = ∫ xy dA
And applying the parallel axis theorem
I xy = I x ' y ' + Ad x d y
Unlike Ix and Iy which always have positive
values [why?] Ixy can be positive or
negative depending on the coordinates of
x and y
Example
Engr210 – Spring 2005
Lesson # 35: Product of Inertia
Example
Instructor: Ahmed Abdel-Rahim
Page 2 of 2