(a) Explanation Calculation: Sketch the diagram of sheet metal as shown in Figure 1. Express the mass ( m ) as shown below: m = ρ V = ρ t A (1) Here, m is mass of the sheet metal, ρ is density sheet metal, t is thickness sheet metal, and A is the area of the sheet metal. Refer to Figure 1. m = ρ t [ ( 2 a ) ( a ) − 1 2 ( 2 a ) ( a 2 ) ] = ρ t [ ( 2 a 2 ) − ( a 2 2 ) ] = ρ t [ 4 a 2 − a 2 2 ] = 3 2 ρ t a 2 ρ t = 2 m 3 a 2 Find the mass moment of inertia mass as shown below: I mass = ρ t I area (2) Substitute 2 m 3 a 2 for ρ t in Equation (2). I mass = 2 m 3 a 2 I area (3) Find the moment of inertia I x , area of about x axis as shown below: I x , area = ( I x ) 1 , area − 2 ( I x ) 2 , area = 1 12 b 1 h 1 3 − 2 ( 1 12 b 2 h 2 3 ) (4) Here, b 1 is width of the rectangular section, h 1 is height of the rectangular section, b 2 is width of the rectangular section, and h 2 is height of the rectangular section (b) To determine Find the mass moment of inertia with respect y axis.

Vector Mechanics for Engineers: Statics, 11th Edition

11th Edition

ISBN: 9780077687304

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek

Publisher: McGraw-Hill Education

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Moment of Inertia

Inertia can be termed as a resistance offered by a body to change its state. A rigid body initially at rest will apply resistance when acted by an external force that tends to change its state of rest or velocity, or a body initially at motion will provi…

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Chapter 9.5, Problem 9.115P

(a)

To determine

Find the mass moment of inertia with respect x axis.

(b)

To determine

Find the mass moment of inertia with respect y axis.

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Chapter 9.5, Problem 9.114P

Chapter 9.5, Problem 9.116P

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Vector Mechanics for Engineers: Statics, 11th Edition

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Find the mass moment of inertia with respect x axis.

Solution Summary: The author explains how to find the mass moment of inertia with respect to x axis.

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