Concept explainers
Moments of Inertia In Exercises 37-40, use the following formulas for the moments of inertia about the coordinate axes of a surface lamina of density
Verify that the moment of inertia of a spherical shell of uniform density about its diameter is
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Chapter 15 Solutions
Calculus: Early Transcendental Functions (MindTap Course List)
- Variable-density solids Find the coordinates of the center of mass of the following solid with variable density. R = {(x, y, z): 0 ≤ x ≤ 4, 0 ≤ y ≤ 1, 0 ≤ z ≤ 1};ρ(x, y, z) = 1 + x/2arrow_forwardElectric charge is distributed over the disk x2+y2=1 so that its charge density is σ(x,y)= 1+x2+y2 (Kl/m2). Calculate the total charge of the disk.arrow_forwarduse spherical coordinates to find the mass of the sphere x2 + y2 + z2 = a2 with the given density'' The density at any point is proportional to the distance between the point and the origin.arrow_forward
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- The vertical stern of a boat partially submerged in seawater with a superimposed coordinate system is shown in the figure. The table shows the widths w of the stern (in feet) at indicated values of y. Use the Midpoint Rule with n = 4 to approximate the fluid force against the stern.arrow_forwardA thin plate covers the triangular region bounded by the x-axis and the lines x = 1 and y = 2x in the first quadrant. The plate’s density at the point (x, y) is δ(x, y) = 6x + 6y + 6. Find the plate’s moments of inertia about the coordinate axes and the origin.arrow_forwardUsing the Divergence Theorem, find the outward flux of F across the boundary of the region D.F = (y-x) i + (z-y) j + (z-x) k ; D: the region cut from the solid cylinder x 2 + y 2 ≤ 49 by the planes z = 0 and z=2 a) 0 b) 98π c) -98π d) -98arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageElementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning