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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 calculate the radius of gyration (k) of the x-component of a triangle, we need to find its moment of inertia (Ix) and its area (A), then use the following formula: k = √(Ix/A) 1. Area (A) of the triangle: A = (1/2) * base * height A = (1/2) * 360mm * 180mm A = 32400 mm² 2. Moment of inertia (Ix) for a triangle: Ix = (1/12) * base * height³ Ix = (1/12) * 360mm * (180mm)³ Ix = (1/12) * 360mm * 5,832,000mm³ Ix = 1,549,440,000 mm⁴ 3. Calculate the radius of gyration (k): k = √(Ix/A) k = √(1,549,440,000 mm⁴ / 32,400 mm²) k = √(47,870 mm²) k ≈ 218.79 mm The radius of gyration of the x-component of the triangle is approximately 218.79mm.
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