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
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter10: Analytic Geometry
Section10.1: The Rectangular Coordinate System
Problem 41E: Find the exact lateral area of each solid in Exercise 40. Find the exact volume of the solid formed...
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Transcribed Image Text:Use cylindrical coordinates to show the indicated characteristic of the cone shown in the figure.
1₂
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 =
= 2 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
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