Explanation Given information: The density of the solid is δ . The radii of the concentric sphere are a and b . Consider the center of the sphere is at the origin. Calculation: Show the spherical coordinate as follows: x = ρ sin ϕ cos θ y = ρ sin ϕ sin θ z = ρ cos ϕ Calculate the moment of inertia of the solid about the z axis as follows: I z = ∫ 0 2 π ∫ 0 π ∫ a b δ ( x 2 + y 2 ) d A = ∫ 0 2 π ∫ 0 π ∫ a b δ ( ρ 2 sin 2 ϕ cos 2 θ + ρ 2 sin 2 ϕ sin 2 θ ) ρ 2 sin ϕ d ρ d ϕ d θ = ∫ 0 2 π ∫ 0 π ∫ a b δ ρ 2 sin 2 ϕ ( cos 2 θ + sin 2 θ ) ρ 2 sin ϕ d ρ d ϕ d θ = ∫ 0 2 π ∫ 0 π ∫ a b δ ρ 4 sin 3 ϕ d ρ d ϕ d θ I z = δ ∫ 0 2 π ∫ 0 π ( ρ 5 5 ) a b sin 3 ϕ d ϕ d θ = δ ∫ 0 2 π

University Calculus: Early Transcendentals (4th Edition)

4th Edition

ISBN: 9780134995540

Author: Joel R. Hass, Christopher E. Heil, Przemyslaw Bogacki, Maurice D. Weir, George B. Thomas Jr.

Publisher: PEARSON

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Chapter 14, Problem 39PE

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Calculate the moment of inertia of the thick sphere.

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Chapter 14, Problem 38PE

Chapter 14, Problem 40PE

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Chapter 14 Solutions

University Calculus: Early Transcendentals (4th Edition)

Ch. 14.1 - In Exercises 1-14. evaluate the iterated...Ch. 14.1 - Prob. 2E Ch. 14.1 - Prob. 3E Ch. 14.1 - In Exercises 1-14, evaluate the iterated...Ch. 14.1 - In Exercises 1-14, evaluate the iterated...Ch. 14.1 - In Exercises 1-14, evaluate the iterated...Ch. 14.1 - In Exercises 1-14, evaluate the iterated integral....Ch. 14.1 - In Exercises 1-14, evaluate the iterated...Ch. 14.1 - In Exercises 1-14, evaluate the iterated integral....Ch. 14.1 - Prob. 10E

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