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Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550

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BuyFindarrow_forward

Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550
Textbook Problem

Assume that the solid has constant density k.

45. Find the moment of inertia about the z-axis of the solid cylinder x2 + y2a2, 0 ≤ zh.

To determine

To find: The momentum of inertia of the solid about the z-axis if the solid has constant density k.

Explanation

Given:

The cylinder is x2+y2a2 and 0zh.

Calculation:

Initially, calculate the moment of inertia over the z-axis. Therefore, the integration will be over (x2+y2)ρ(x,y,z) but here the density is constant.

The moment of inertia over the z-axis is, Iz=E(x2+y2)ρ(x,y,z) dV.

Iz=k02π0h0a(r2)rdrdzdθ

Integrate the above integral with respect to r and apply the limit of it.

Iz=k02π0h0a(r3)drdzdθ=k02π0h[r44]0adzdθ=k02π0h[a</

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Chapter 15 Solutions

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