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Determine the moment of inertia and the radius of gyration of the shaded area shown with respect to the $x$ axis.
Physics 101 Mechanics
Chapter 9
Distributed Forces: Moments of Inertia
Section 1
Moments of Inertia of Areas
Moment, Impulse, and Collisions
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we'll ask to determine the second moment of area and the radius sub duration of the shaded area shown with respect to the X axis. The area is bordered by why because K X square we know that at X equals two a. Why is aged okay? Was h over for a square theater? Go we need to do is integrating y squared over the area and that area goes from y equals zero to y of X and X equals zero r A to a And if we crank through those in a girl's with not pretty but we can do it We get that ice of X equals 127 over 1344 eight times eight cube. And if we Catholic the numerically we get 0.9458 cube the area Can you if we just plug in one here we get the area and do these in a girls and we get that that is 7/12 h and then the radius of gyration. And this was respect to X access is, um, square root of this divided by this. So we get that that turns out to be square root of 1 27 all over 28 times H, or 0.40 to H.
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