2. Find the moment of inertia, radii of gyration and product of inertia considering the figure lies on the first quadrant. Note that there is a shaded region on the semicircular part. y 50 mm 30 mm 30 mmi 上 .40 mm-
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Q: 1. Find the moment of inertia, radii of gyration and product of inertia. 60 30 25 90 20 80…
A: A1=60×30=900mm2x1=30mmh1=55mmA2=25×90=2250mm2x2=12.5mmh2=0A3=80×20=1600mm2x3=40mmh3=60mm
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A: Given, a = 10 mm
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Q: Solve for the maximum and minimum moment of inertia. 300mm 300mm 400mm 200mm
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- Using Ix and Iu from Table 9.2, determine the moment of inertia of the circular sector about the OB-axis. Check your result for =45 with that given for a quarter circle in Table 9.2.Find the moments of inertia Ix, Iy, I0 for a lamina in the shape of an isosceles right triangle with equal sides of length a if the density at any point is proportional to the square of the distance from the vertex opposite the hypotenuse. (Assume that the coefficient of proportionality is k, and that the lamina lies in the region bounded by x = 0, y = 0, and y = a − x).Ix = Iy = I0 =Calculate and determine the Moments and Principal Axes of Inertia of the profile below, indicating the best position to use the profile.Where:h = 21 cmb = 28 cm
- Determine the moments of inertia and the product of inertia of the L3 x 2 x 1/4-14 angle cross section of Prob. 9.74 with respect to new centroidal axes obtained by rotating the x and y axes 30° clockwise.(Reference to Problem 9.75):Using the parallel-axis theorem, determine the product of inertia of the area shown with respect to the centroidal x and y axes.Consider a circular, semi-circular, and a quarter-circular steel plate, whose moment of inertia about the z-axis are Izc, Izs, and Izq, respectively. They have equal mass densities and thicknesses. Which of the following is correct? a. Izc=Izs greater than Izqb. Izcgreater thanIzs=Izqc.Izcgreater thanIzsgreater thanIzqUsing the polar moment of inertia of the isosceles triangle of Prob. 9.28, show that the centroidal polar moment of inertia of a circular area of radius r is π4/2. ( Hint: As a circular area is divided into an increasing number of equal circular sectors, what is the approximate shape of each circular sector?)(Reference to Problem 9.28):Determine the polar moment of inertia and the polar radius of gyration of the isosceles triangle shown with respect to point O.
- the ratio moment of inertia of a rectangular shape to triangular shape having the same base width(b) and height(h) with respect to the baseline would beCalculate and determine the Moments and Principal Axes of Inertia of the profiles below, indicating the best position to use the profile.h = 21 cmb = 28 cmThe mass moment if inertia of a cylinder about its central axis perpendicular to a circular cross section is
- Suppose that a = 1.21 m and b = 1.1 m . (Figure 1) Determine the moment of inertia for the shaded area about the x axis. Express your answer to three significant figures and include the appropriate units.Two identical solid spheres are attached on the 2cm diameter solid rod with the density of 7750 'kg/m³. Calculate moment inertia about P- P axis of a lamina. The measurements are in cm. 3 kg 5 kg 10 cm 50 cm 40 cmFor the area indicated, determine the orientation of the principal axes at the origin and the corresponding values of the moments of inertia.Area of Prob. 9.73(Reference to Problem 9.73):Using the parallel-axis theorem, determine the product of inertia of the area shown with respect to the centroidal x and y axes.