Last Updated on September 8, 2026 by Maged kamel
Video for a product of inertia-right-angle case 2.
How can we derive an expression for the product of inertia at the intersection of the base and the Y axis at the left side of the right-angle case 2?
Two methods are used to find the value of Ixy. The first method uses a vertical strip, while the second uses a horizontal strip.
For Ixy estimation, we use a horizontal strip; the strip width is (b-x), and its height is y.
2- Since the strip height starts from the base and intersects with line AC, the y value is the same as the line AC equation y=h*x/b, for x value it will be=b*y/h.
3- the product moment of inertia due to that strip dIxy=dA*xbar*ybar), our x bar =((x+0.50*(b-x))=1/2(b+x), while ybar=y. Since we are integrating in the y direction, we will substitute for the x value as (x=b*y/h ). We integrate from x=0 to x=b, and the final answer is Ixy = h^2*b^2/8, the same value obtained using a horizontal strip.
Timestamps for the video:
- 0:00- How to derive the expression for the product of inertia for a right-angle triangle case -2? Case of a vertical strip.
- 3:10- The value of Ixy for a right-angle triangle case -2 with a vertical strip.
- 4:00- How to derive the expression for the Product of Inertia for a right-angle triangle case -2? Case of HL strip.
- 8:00- The value of Ixy for a right-angle triangle case -2 with a vertical strip.
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For an external resource, the definition of the moment of inertia with solved problems, and the 2nd moment of inertia.
The previous video is 15-Video-Iy and polar moment of inertia-right angle-case 2.
The related post is post-12: Product of inertia Ixy for the right-angle case 2.
The next video is no. 17, a Video for Ixy in the CG-right-angle case 2.