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

2024
Views:

162

Pages:

2
Author:

omiliar74be

COSMOS: Complete Online Solutions Manual Organization System Chapter 9, Solution 138. First compute the mass of each component. Have m = ρ stV = ρ st tA ( ) m1 = 7850 kg/m 3 ( 0.003 m )( 0.70 m )( 0.780 m ) = 12.858 kg  π  2 m2 = 7850 kg/m 3 ( 0.003 m )   ( 0.39 m )  = 5.6265 kg  2   ( )  1   m3 = 7850 kg/m 3 ( 0.003 m )   ( 0.780 m )( 0.3 m )  = 2.7554 kg 2    ( ) Using Fig. 9.28 for component and the equations derived above for components and have I x = ( I x )1 + ( I x )2 + ( I x )3 2 1 2  0.78   2 = (12.858 kg )  ( 0.78 ) +   m  2   12 2   1 16  2  4 × 0.39  2  2 0.39 + ( 5.6265 kg )  − +  )   + ( 0.39 )   m 2 (  3π     2 9π   0.78 2  0.30 2   2 2 2 1 + ( 2.7554 kg )  ( 0.78) + ( 0.30 )  +  +   m   3  18   3     = ( 2.6076 + 1.2836 + 0.3207 ) kg ⋅ m 2 = 4.2119 kg ⋅ m 2 or I x = 4.21 kg ⋅ m 2 continued COSMOS: Complete Online Solutions Manual Organization System And ( )1 + ( I y )2 + ( I y )3 Iy = Iy 1 2 2 2 2  1 = (12.858 kg )  ( 0.7 ) + ( 0.78 )  + ( 0.7 ) + ( 0.78)   m 2  4  12  2 2 1 + ( 5.6265 kg )  ( 0.39 ) + ( 0.39 )  m 2 4   2  1  2 2  0.78    4 + ( 2.7554 kg )  ( 0.78 ) + ( 0.7 ) +    m 18  3      = ( 4.7077 + 1.0697 + 1.6295 ) kg ⋅ m 2 = 7.4069 kg ⋅ m 2 or I y = 7.41 kg ⋅ m 2 And I z = ( I z )1 + ( I z )2 + ( I z )3  1  2 1 = (12.858 kg ) ( 0.7 )  +  m 2  12 4    2 1 + ( 5.6265 kg )  ( 0.39 )  m 2 4   2  1  2 2  0.30    2 + ( 2.7554 kg )  ( 0.3) + ( 0.70 ) +    m 18  3      = ( 2.1001 + 0.21395 + 1.39145 ) kg ⋅ m 2 = 3.7055 kg ⋅ m 2 or I z = 3.71 kg ⋅ m 2