Chapter 10, Problem 74P

By the method of this article, determine the moments of inertia about the x-and y-axes of the trapezoidal area. 1.5b 1.5b 1.3b b Answers: Ix= i ba ba

1. Determine the moment of inertia of the shaded section about its horizontal and vertical components. 3"- -3"· - 6" 1"

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 = 10 in. 9" 33" h Amswers: (a) h = 0 Ix = in.4 (b) h = 10 in. Ix = i in.4

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 moment of inertia and the radius of gyration of the shaded area shown with respect to the x axis.

Determine the moment of inertia and the radius of gyration of the shaded area with respect to the x-axis. Given: a = 11.4 mm. 8 mm- 24 mm -24 mm 6 mm 24 mm 24mm The moment of inertia is The radius of gyration is 6 mm 10³ mm4. mm.

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 ✔

The moments of inertia about the x- and u-axes of the plane region areIx = 14 × 10^9 mm^4 and Iu = 38 × 10^9 mm^4, respectively. If h = 200 mm, determine the area of the region, and the radius of gyration about the centroidal axis parallel to the x-axis.

Determine the moment of inertia of the composite area about the x- and y- axes. y Answer: 1x = 209 in4 ly = 533 in4 T 3 in. 3 in. -3 in. 6 in. X I