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Question: Calculate the radius of gyration of the x component of a triangle with base of 360mm and height 180mm if the triangle is located on the X and Y axis.
To find the radius of gyration of the x-component of the triangle, we first need to find the moment of inertia (Ix) about the x-axis. The formula for the moment of inertia of a triangle about its base-axis (x-axis) is: Ix = (base * height^3) / 36 Here, base = 360mm and height = 180mm. Plug the values into the formula: Ix = (360 * 180^3) / 36 Ix = (360 * 5832000) / 36 Ix = 2101248000 / 36 Ix = 58368000 mm^4 Next, we need to find the area of the triangle: Area = (base * height) / 2 Area = (360 * 180) / 2 Area = 32400 mm^2 Now, we can find the radius of gyration (kx) for the x-component: kx = √(Ix / Area) kx = √(58368000 / 32400) kx = √1805 kx ≈ 42.49mm (rounded to two decimal places) So, the radius of gyration of the x-component of the triangle is approximately 42.49 mm.
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