Chapter 10, Problem 72P

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. -0.80h Answers: lx = i ly= i lo = i 0.67h -0.80h h4 h4 h4

The shaded area has the following properties: 4 = 126 x10 mm* ; 1, = 6,55 x10* mm* ; and Pay =-1.02 10° mm* Determine the moments of inertia of the area about the x' and v' axes if e=30°.

Determine the centroid and the moment of inertia about an x-axis passing through the centroid for the geometry below. 25 mm Ľ X Ø50 mm 5 mm 100 mm $50 mm 80 mm

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 and the radius of gyration of the shaded area with respect to the x-axis. Given: r = 79 mm. 125 mm 125 mm - 250 mm The moment of inertia is The radius of gyration is *106 mm4. mm.

Determine the moments of inertia of the shaded area with respect to the x and y axes. use a horizontal differential element of thickness for both calculations.

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

The variable h designates the arbitrary vertical location of the center of the circular cutout within the semicircular area. Determine the area moment of inertia about the x-axis for (a) h = 0 and (b) h = 3 in. 2" 7" h Amswers: (a) h = 0 in.4 (b) h = 3 in. Ix = in 4

H6. Find the position of the cross-section’s centroid. Then, determine the moments of inertia of horizontal & vertical axes through the centroid.   (I'm not sure if the width of the verticle rectangle is needed or not. If it is, assume 5 mm.)