![]() In this lesson, we will learn how to derive the formula as well as its application in problems. So again, I x why went from positive to negative almost with the same value, but an absolute value. Moment of inertia of a quarter circle is usually found or calculated using the given formula I R 4 / 16. So we get here 1033 interests to the fore and we can figure out again the height, the distance here because we know the radius that we know the angle and that is this is that minus 873 inches to the fourth. And this gives us We know that we know again we know this angle here and this radio. So that gives us 2021 inches to the fourth. We know the radius and we know this angle. Since we know again, we just have this triangle here. And so then we want to go 120 degrees on more circle around this way, so that gives us 60 point five degrees and so Now it's just a matter of doing the geometry to find this point. And that gives us 1000 and three interest in the fourth. ![]() We can calculate because we know this point and we know at this point and so we can calculate that. ![]() ![]() And we know that the center is at the average of these two things, so that's 1527 inches to the fourth. We know the area moments in the area, product about these access, and we know the angle through the principal axes, and that's about 30 degrees down here. So from previous problems, we know all this information. So no, but something like use active is here. And we want to rotate the axes by 60 degrees counterclockwise. So here we're looking to use more circle to, um see how a axes rotation effects the area moments in the area product for this cross section.
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