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Find the radius of gyration of a plate covering the region bounded by y=3x, x=2, and the x-axis with respect to the y-axis.

Find the radius of gyration of a plate covering the region bounded by y=3x, x=2, and the x-axis with respect to the y-axis.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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If the plate has moment of inertia ly and mass m, then the radius of gyration R, is given by the following formula. ly Ry Therefore, the next step is to compute the mass of the plate. Recall that the mass of a plate equals its density times its area. 2 m = k y = 0 2 kf (7x³) dx 0 = 7k = 28k R² dx Finally, compute the radius of gyration. ly Ry Ry = 2 = 224k 1 3 2√6 3 X 28k 2√6 Therefore, if all of the mass of the plate were at a distance of from the 3 y-axis, the moment of inertia about the y-axis would be the same as the moment of inertia of the plate itself.
Transcribed Image Text:If the plate has moment of inertia ly and mass m, then the radius of gyration R, is given by the following formula. ly Ry Therefore, the next step is to compute the mass of the plate. Recall that the mass of a plate equals its density times its area. 2 m = k y = 0 2 kf (7x³) dx 0 = 7k = 28k R² dx Finally, compute the radius of gyration. ly Ry Ry = 2 = 224k 1 3 2√6 3 X 28k 2√6 Therefore, if all of the mass of the plate were at a distance of from the 3 y-axis, the moment of inertia about the y-axis would be the same as the moment of inertia of the plate itself.
Find the radius of gyration of a plate covering the region bounded by y = 3x³, x=2, and the x-axis with respect to the y-axis. R₁ =
Transcribed Image Text:Find the radius of gyration of a plate covering the region bounded by y = 3x³, x=2, and the x-axis with respect to the y-axis. R₁ =
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y=3x3   x=2   

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