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Determine the moment of inertia and the radius of gyration of the shaded area with respect to the $y$ axis.

Physics 101 Mechanics

Chapter 9

Distributed Forces: Moments of Inertia

Section 2

Parallel-Axis Theorem and Composite Areas

Moment, Impulse, and Collisions

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we have to find the area moment and radio driving radius of gyration of this cross section again. But now about the y axis with the y axis goes up the center here. This one's easy. Because this why access passes through the central rate of all of our pieces of our geometry here. So we just have, you know, 1 12 HB cubed or, um, basically all on all of these cases where this is the, um, base or the Here's Yeah, here's the height h on this is being. And so if we plug in those values from the what we get from our from the dimension from the book, you get that this is zero point, as you are, too. 0.2 05 centimeters to the fourth. This one up here is your 0.691 centimeters for the fourth. And this one here is five point, um, 53 centimeters to the fourth, and we can see that this one is quite a bit larger because again, it has a lot of area away from this x axis. So we at we had all these up and we get that the area moment about the Y axis is six point to 4 to 6 centimeters to the fourth. The area we have from before and so we can get the radius of gyration about the Y Axis is 0.887 senators.

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