Explanation Given: The mass per unit area of the material is 20 kg / m 2 . Subdivide the segment into 2 parts: Part 1: Plate Part 2: Four similar holes Show the free body diagram of the subdivided segments as in Figure 1. Calculations: From Figure 1, Calculate the diastance of point O from the center of the thin plate. d = ( 400 mm ) sin 45 ° = [ ( 400 mm ) 1 m 1 , 000 mm ] sin 45 ° = 0.4 sin 45 ° = 0.2828 m Calculate the mass of segment 1. m 1 = ( 400 mm ) ( 400 mm ) ( 20 kg / m 2 ) = [ ( 400 mm ) 1 m 1 , 000 mm ] [ ( 400 mm ) 1 m 1 , 000 mm ] ( 20 kg / m 2 ) = ( 0.4 m ) ( 0.4 m ) ( 20 kg / m 2 ) = 3.2 kg Calculate the mass of segment 2. m 2 = π ( 50 mm ) 2 ( 20 kg / m 2 ) = π [ ( 50 mm ) 1 m 1 , 000 mm ] 2 ( 20 kg / m 2 ) = π ( 0.05 m ) 2 ( 20 kg / m 2 ) = 0.1570 kg Calculate the mass moment of inertia of the plate about an axis perpendicular to the page and passing through the point C . I C = 1 2 m 1 ( 400 mm 2 + 400 mm 2 ) − 4 [ 1 2 m 2 ( 50 mm ) 2 + m 2 ( 150 mm ) 2 ] (I) Substitute 3 .2 kg for m 1 and 0 .1570 kg for m 2 in Equation (I)

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ISBN: 9780135681879

Author: HIBBELER

Publisher: PEARSON

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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 10.8, Problem 99P

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The mass moment of inertia of the thin plate.

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Chapter 10.8, Problem 98P

Chapter 10.8, Problem 100P

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The mass moment of inertia of the thin plate.

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