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

2019
Views:

261

Pages:

2
Author:

Dixie Summers

COSMOS: Complete Online Solutions Manual Organization System Chapter 9, Solution 174. First compute the mass of each component. m = ( m/L ) L Have = ( 0.049 kg/m ) L m1 = ( 0.049 kg/m )( 2π × 0.32 m ) Then = 0.09852 kg m2 = m3 = m4 = m5 = ( 0.049 kg )( 0.160 m ) = 0.00784 kg I x′y′ = I y′z′ = I z′x′ = 0 for each component. Now observe that x1 = x4 = x5 = 0, Also, y1 = 0, z1 = z2 = z3 = 0 Then ( 0 ) I xy = Σ I x′y′ + mx y = m2 x2 y2 + m3x3 y3 = ( 0.00784 kg ) ( 0.32 m )( 0.08 m ) + ( 0.24 m )( 0.16 m )  = 0.50176 × 10−3 kg ⋅ m 2 By symmetry Now I yz = I xy = 0.50176 × 10−3 kg ⋅ m 2 I zx = Σ ( I z′x′ + mz x ) = 0 From the solution to Problem 9.148 I x = I z = 6.8505 × 10−3 kg ⋅ m 2 I y = 12.630 × 10−3 kg ⋅ m 2 continued COSMOS: Complete Online Solutions Manual Organization System λ OL = Now 1 ( −3i − 6 j + 2k ) 7 Have 0 I OL = I xλx2 + I y λ y2 + I z λz2 − 2 I xy λxλ y − 2I yz λ y λz − 2I zxλz λx  Eq. ( 9.46 )    3 2  2 2   = ( 6.8505 )  −  +     × 10−3 kg ⋅ m 2  7      7  2    6 + (12.63)  −   × 10−3 kg ⋅ m 2  7     3  6   6  2    −2 ( 0.50176 )  −  −  +  −     × 10−3 kg ⋅ m 2  7  7   7  7   = (1.8175 + 9.2792 − 0.12288 ) × 10−3 kg ⋅ m 2 = 10.9738 × 10−3 kg ⋅ m 2 or I OL = 10.97 × 10−3 kg ⋅ m 2