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

2021
Views:

72

Pages:

2
Author:

crawniadxfo

COSMOS: Complete Online Solutions Manual Organization System Chapter 9, Solution 153. Have m = ρalV Then kg   m1 =  2700 3  ( 0.350 × 0.100 × 0.030 ) m 3 m   = 2.8350 kg kg   m2 =  2700 3  ( 0.200 × 0.100 × 0.050 ) m 3 m   = 2.7000 kg kg  2  m3 =  2700 3  π ( 0.025) × 0.100  m3   m   = 0.53014 kg First note that symmetry implies I x′y′ = I y′z ′ = I z ′x′ = 0 for each component Now I uv = I u ′v′ + mu v where I u′v′ = 0 I xy = Σmx y = ( 2.8350 kg )( 0.175m )( 0.050 m ) + ( 2.7000 kg )( 0.100 m )( 0.050 m ) − ( 0.53014 kg )( 0.080 m )( 0.050 m ) = ( 24.806 + 13.500 − 2.1206 ) × 10−3 kg ⋅ m 2 = 36.1854 × 10−3 kg m 2 or I xy = 36.2 × 10−3 kg ⋅ m 2 I yz = Σmy z = ( 2.8350 kg )( 0.050 m )( 0.015m ) + ( 2.7000 kg )( 0.050 m )( 0.055m ) − ( 0.53014 kg )( 0.050 m )( 0.040 m ) = ( 2.1263 + 7.4250 − 1.06028 ) × 10−3 kg ⋅ m 2 = 8.49102 × 10−3 kg ⋅ m 2 or I yz = 8.49 × 10−3 kg ⋅ m 2 continued COSMOS: Complete Online Solutions Manual Organization System I zx = Σmz x = ( 2.8350 kg )( 0.015m )( 0.175m ) + ( 2.7000 kg )( 0.055m )( 0.100 m ) − ( 0.53014 kg )( 0.040 m )( 0.080 m ) = ( 7.4419 + 14.850 − 1.69645 )10−3 kg ⋅ m 2 = 20.59545 × 10 −3 kg ⋅ m 2 or I zx = 20.6 × 10−3 kg ⋅ m 2