Use cylindrical coordinates to show the indicated characteristic of the cone shown in the figure. I₂ h gives k = z=h To Assume that the cone has uniform density p(x, y, z) =k and show that the moment of inertia about the z-axis is ¹₂ = = 23 mr ². Begin by setting up and evaluating the triple integral for I₂. Submit Answer To y Using the formula for the volume of right circular cones, the volume of this cone is V = Substituting for k in I, and simplifying shows that I₂ =mr ². dz dr de . Substituting this into the mass equation m = kV and solving for k
Use cylindrical coordinates to show the indicated characteristic of the cone shown in the figure. I₂ h gives k = z=h To Assume that the cone has uniform density p(x, y, z) =k and show that the moment of inertia about the z-axis is ¹₂ = = 23 mr ². Begin by setting up and evaluating the triple integral for I₂. Submit Answer To y Using the formula for the volume of right circular cones, the volume of this cone is V = Substituting for k in I, and simplifying shows that I₂ =mr ². dz dr de . Substituting this into the mass equation m = kV and solving for k
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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