Explanation Given information: The density ( δ ) is 1. The plate bounded by the y -axis and the lines y = 2 x and y = 4 in the xy plane. Calculation: Calculate the polar moment of inertia about the origin as shown below. I o = ∬ R δ ( x 2 + y 2 ) d A Substitute 3 for δ , dydx for dA and apply the limits as shown below. I o = ∫ 0 2 ∫ 2 x 4 3 ( x 2 + y 2 ) d y d x = 3 ∫ 0 2 ( x 2 y + y 3 3 ) 2 x 4 d x = 3 ∫ 0 2 ( x 2 ( 4 ) + 4 3 3 − ( <

University Calculus: Early Transcendentals (3rd Edition)

3rd Edition

ISBN: 9780321999580

Author: Joel R. Hass, Maurice D. Weir, George B. Thomas Jr.

Publisher: PEARSON

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Chapter 14, Problem 16AAE

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Calculate the polar moment of inertia of the plate about the origin.

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Chapter 14, Problem 15AAE

Chapter 14, Problem 17AAE

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Chapter 14 Solutions

University Calculus: Early Transcendentals (3rd Edition)

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