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

2023
Views:

170

Pages:

2
Author:

behend6abs

COSMOS: Complete Online Solutions Manual Organization System Chapter 9, Solution 149. m = ρV = ρ AL Have Then ( ) 2 m1 = m2 = 7850 kg/m 3 π ( 0.0015 m )  × (π × 0.36 m )   m2 = m1 = 0.062756 kg ( ) 2 m3 = m4 = 7850 kg/m 3 π ( 0.0015 m )  × ( 0.36 m )   = 0.019976 kg Using the equations given above and the parallel axis theorem, have I x = ( I x )1 + ( I x )2 + ( I x )3 + ( I x )4 where ( I x )3 = ( I x )4 Then 2 2 2 1 1 I x = ( 0.062756 kg )  ( 0.36 m )  + ( 0.062756 )  ( 0.36 m ) + ( 0.36 m )  2  2  2 2 2 1 + 2 ( 0.019976 kg )  ( 0.36 m ) + ( 0.18 m ) + ( 0.36 m )  12   =  4.06659 + 12.19977 + 2 ( 3.45185 )  × 10−3 kg ⋅ m 2 = 23.1701 × 10−3 kg ⋅ m 2 or I x = 23.2 × 10−3 kg ⋅ m 2 Have where ( )1 + ( I y )2 + ( I y )3 + ( I y )4 Iy = Iy ( I y )1 = ( I y )2 and ( I y )3 = ( I y )4 continued COSMOS: Complete Online Solutions Manual Organization System ` Then 2 2 I y = 2 ( 0.062756 kg ) ( 0.36 m )  + 2 ( 0.019976 kg ) 0 + ( 0.36 m )      ( ) ( = 2 8.13318 × 10−3 kg ⋅ m 2 + 2 2.58889 × 10 −3 kg ⋅ m 2 ) = 21.44414 × 10−3 kg ⋅ m 2 or I y = 21.4 × 10−3 kg ⋅ m 2 Have I z = ( I z )1 + ( I z )2 + ( I z )3 + ( I z )4 where ( I z )3 = ( I z )4 Then 2 1 I z = ( 0.062756 kg )  ( 0.36 m )  2  2  1 4  2  2 × 0.36 m  2 + ( 0.062756 kg )  − 2  ( 0.36 m ) +  + 0.36 m  ( )  π    2 π   2 1 + 2 ( 0.019976 kg )  ( 0.36 m )  3   =  4.06659 + 12.1998 + 2 ( 0.86296 )  10−3 kg ⋅ m 2 = 17.9923 × 10−3 kg ⋅ m 2 or I z = 17.99 × 10−3 kg ⋅ m 2