COSMOS Chapter 9 Solution 155 | Michigan State University - Edubirdie

University:
Michigan State University
Course:
ERG 160 | Success in Science, Technology, Engineering, and Mathematics
Academic year:

2019
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63

Pages:

2
Author:

Tarime9wn

COSMOS: Complete Online Solutions Manual Organization System Chapter 9, Solution 155. m = ρV Have = ρ tA kg   m1 =  7860 3  ( 0.003 m )( 0.2 × 0.090 ) m 2 m   Then = 424.44 × 10−3 kg kg  π 2  m2 =  7860 3  ( 0.003 m ) × ( 0.045 m ) 2 m   = 75.005 × 10−3 kg I uv = I u′v′ + m u v Now I x′y′ = I y′z ′ = I z ′x′ = 0 Symmetry implies ∴ Then for both elements. Iuv = ∑ miui v i ( ) ( ) I xy = 424.44 × 10−3 kg ( 0.050 m )( 0.045 m ) + 75.005 × 10 −3 kg ( − 0.050 m )( 0.045 m ) ( ) = 954.99 × 10−6 − 168.761 × 10−6 kg ⋅ m 2 = 786 × 10−6 kg ⋅ m 2 I xy = 786 × 10−6 kg ⋅ m 2 continued COSMOS: Complete Online Solutions Manual Organization System  4 × 0.045  I yz = 424.44 × 10−3 kg ( 0.045 m )( 0 ) + 75.005 × 10−3 kg ( 0.045 m )  m 3π   ( ) ( ) = 64.5 × 10−6 kg ⋅ m 2 I yz = 64.5 × 10−6 kg ⋅ m 2  4 × 0.045  I zx = 424.44 × 10−3 kg ( 0 )( 0.050 m ) + 75.005 × 10−3 kg  m  ( − 0.050 m ) 3π   ( ) = − 71.6 × 10−6 kg ⋅ m 2 ( ) I zx = − 71.6 × 10−6 kg ⋅ m 2

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