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

2024
Views:

135

Pages:

1
Author:

Sean Horton

COSMOS: Complete Online Solutions Manual Organization System Chapter 9, Solution 131. Consider shell to be formed by removing hemisphere of radius r hemisphere of radius r + t. For hemisphere: from I = 2 2 mr 5 m = ρV = Area = 1 4π r 2 = 2π r 2 2 ( ) 1 4 3 2 ρ π r = ρπ r 3 2 3 3 I = Thus 2 2 4 3 2 ρπ r 5  ρπ r  r = 53 15  For hemispherical shell: I = 4 4 5 ρπ ( r + t ) − r 5  = ρπ  r 5 + 5r 4t + 10r 3t 2 + ... − r 5    15 15 Neglect terms with powers of t > 1, I = 4 ρπ r 4t 3 Mass of shell: ( I = 2 ρπ r 2t ( ) m = ρV = ρ tA = ρ t 2π r 2 = 2 ρπ r 2t ) 23 r 2 = 2 2 mr 3 I = 2 2 mr 3 Radius of gyration: k2 = I 2 = r2 m 3 k = 0.816r

COSMOS Chapter 9 Solution 131

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