Explanation Given information: The density of steel is 7 , 850 kg / m 3 . The thickness of sheet steel is 2 mm . Calculation: Sketch the sheet steel as shown in Figure 1. Find the mass of the component 1 as shown below: m 1 = ρ ST V = ρ ST ( t A ) (1) Here, ρ ST is density of steel, V is the volume of component 1, t is thickness of sheet steel, and A is the area of sheet section. Find the rectangular area of sheet steel section as shown in below. A = b × h (2) Here, b is the width of the section and h is the height of the section. Substitute 0.76 m for b and 0.48 m for h in Equation (2). A = 0.76 × 0.48 = 0.3648 m 2 Substitute 7 , 850 kg / m 3 for ρ ST , 2 mm for t , and 0.3648 m 2 for A in Equation (1). m 1 = 7 , 850 ( 2 mm ( 1 m 10 3 mm ) × 0.3648 ) = 7 , 850 × 0.002 × 0.3648 = 5.72736 kg Find the mass of the component 2 as shown below: m 2 = ρ ST V = ρ ST ( t A ) = ρ ST ( t ( 1 2 b h ) ) (3) Substitute 7 , 850 kg / m 3 for ρ ST , 2 mm for t , and 0.76 m for b and 0.48 m for h in Equation (3). m 2 = 7 , 850 ( 2 mm ( 1 m 10 3 mm ) ) ( 1 2 × 0.76 × 0.48 ) = 7 , 850 × 0.002 × 0.1824 = 2.86368 kg Find the mass of the component 3 as shown below: m 3 = ρ ST V = ρ ST ( t A ) = ρ ST ( t ( π 4 r 2 ) ) (4) Substitute 2 mm for t 7 , 850 kg / m 3 for ρ ST , and 0.48 m for r in Equation (4). m 3 = 7 , 850 × 0.002 × ( π 4 × 0.48 2 ) = 7 , 850 × 0.002 × 0.180955 = 2.84101 kg Find the mass moment of inertia with respect to x axis using the relation as shown below: I x = ( I x ) 1 + ( I x ) 2 + ( I x ) 3 = [ ( 1 12 × m 1 d 2 + m 1 ( d 2 ) 2 ) + 1 18 m 2 d 2 + m 2 ( d 3 ) 2 + 1 2 m 3 × d 2 ] (5) Substitute 5.72736 kg for m 1 , 2.86368 kg for m 2 , 2.84101 kg for m 3 , and 0.48 m for h in Equation (5). I x = [ ( 1 12 × 5.72736 × 0.48 2 + 5.72736 × ( 0.48 2 ) 2 ) + 1 18 × 2.86368 × 0.48 2 + 2.86368 ( 0.48 3 ) 2 + 1 2 × 2

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ISBN: 9781265566296

Author: BEER

Publisher: MCG

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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, Problem 9.195RP

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Find the mass moment of inertia with respect to x,y,z axis.

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Chapter 9, Problem 9.194RP

Chapter 9, Problem 9.196RP

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A section of sheet steel 2 mm thick is cut and bent into the machine component shown. Knowing that the density of steel is 7850 kg/m3 , determine the mass products of inertia Ixy, Iyz, and Izx of the component.

A 2-mm thick piece of sheet steel is cut and bent into the machine component shown. Knowing that the density of steel is 7850 kg/m3 , determine the mass moment of inertia of the component with respect to each of the coordinate axes.

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Find the mass moment of inertia with respect to x , y , z axis.

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