Chapter 10, Problem 79P

Determine the moments of inertia of the shaded area about the x- and y-axes. Also determine the polar moment of inertia about point O. -0.56h Answers: 1x = i ly= i lo= i 0.60h -0.56h h h4 h4 he

Determine the moment of inertia of the above section (Fig. 1) about Ox axis.

P6-30 6-31. Determine the moment of inertia of the shaded area of Fig. P6-31 with respect to the y axis. 3" 2 4" P6-31

Determine the moments of inertia of the Z-section about its centroidal x0- and y0-axes.

Find the moment of inertia about the x-axis of a thin plate bounded by the parabola x = 7y - 3y² and the line x + 2y = 0 if 8(x,y) = x + 2y. Choose the correct sketch of the plate described above. O A. Q O A. SS F(x,y) dy dx O B. OB. F(x,y) dx dy Q Select the order of integration that will make the computations easier and fill in the limits of integration in your choice. G O C. O D. Use the given density function 8 to write the appropriate integrand F(x,y) for finding the moment of inertia. Then substitute into the correct integral from the previous step and evaluate to find the moment of inertia for the plate. The moment of inertia is (Simplify your answer.) Q Q ✔

Determine the moments of inertia of the rectangular area about the x- and y-axes and find the polar moment of inertia about point O. Assume ho = 0.34h, bo = 0.16b. y | h h. b Answers: bh3 %3D ly = i hb3 Iz = i bh3 + i hb3

Determine the moments of inertia of the shaded area about the x- and y-axes. Also determine the polar moment of inertia about point O. -0.44h -0.44h 0.74h h Answers: Ix = h4 Iy = h4 Io = 4

1. Determine the moment of inertia about an axis perpendicular to the page and passing through the pin at 0. The thin plate has a hole in its center. Its thickness is 50 mm, and the material has a density of p = 60 kg/m³. What is the radius of gyration about this point? 150 mm 1.40 m 1.40 m

Formulas Moments of Inertia x= [y²d ly = fx²dA Theorem of Parallel Axis Ixr = 1 + d² A * axis going through the centroid x' axis parallel to x going through the point of interest d minimal distance (perpendicular) between x and x' ly₁ = 15+d²A ỹ axis going through the centroid y' axis parallel to y going through the point of interest d minimal distance (perpendicular) between y and y' Composite Bodies 1=Σ 4 All the moments of inertia should be about the same axis. Radius of Gyration k=