Explanation Given: Solid region is defined as w = [ − a , a ] × [ − a , a ] × [ 0 , H ] of total mass M Key points: • Moment of Inertia is the sum of the products of the mass of the each particle in the body with the square of distance from the axis of rotation Calculation: Consider box w = [ − a , a ] × [ − a , a ] × [ 0 , H ] Total mass = M density = mass volume ⇒ ρ = M V ⇒ d m = ρ d v ⇒ density = ρ = M ( 2 a ) 2 H = M 4 a 2 H d m = ρ d v = ρ d v Moment of inertia of box of small mass d m ⇒ d I = x 2 d m ⇒ I = ∫ − a a x 2 d m ⇒ I = ∫ − a a x 2 d m ρ = d m

4th Edition

ISBN: 9781319055844

Author: FRANZOSA

Publisher: VST

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Chapter 16.5, Problem 44E

To determine

To calculate:

The moment of inertia $I_{z}$ of the box

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Chapter 16.5, Problem 43E

Chapter 16.5, Problem 45E

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Chapter 16 Solutions

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The moment of inertia I z of the box

Solution Summary: The author explains how the moment of inertia of the box is calculated by dividing the mass of each particle with the square of distance from the axis of rotation.

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The moment of inertia $I_{z}$ of the box

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Chapter 16 Solutions

The moment of inertia I z of the box

Solution Summary: The author explains how the moment of inertia of the box is calculated by dividing the mass of each particle with the square of distance from the axis of rotation.

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To calculate: The moment of inertia Iz of the box

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Chapter 16 Solutions

To calculate:

The moment of inertia $I_{z}$ of the box