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

2024
Views:

418

Pages:

2
Author:

Tyshawn Shaffer

COSMOS: Complete Online Solutions Manual Organization System Chapter 9, Solution 173. First compute the mass of each component m = ρ stV = mAL Have ( ) 2 = 7850 kg/m 3 π ( 0.0015 m )  L   = ( 0.055488L ) kg/m m1 = m2 = 0.055488 kg/m (π × 0.36 m ) Then = 0.062756 kg m3 = m4 = 0.055488 kg/m ( 0.36 m ) = 0.019976 kg Now observe that the centroidal products of inertia I x′y′ = I y′z ′ = I z′x′ = 0 for each component. x3 = x4 = 0, Also y1 = 0, z1 = z2 = 0 Then ( 0 ) I xy = Σ I x′y′ + mx y = m2x2 y2  2 × 0.36 m  2 −3 = ( 0.062756 kg )  −  ( 0.36 m ) = −5.1777 × 10 kg ⋅ m π   ( 0 ) I yz = Σ I y′z ′ + my z = m3 y3 z3 + m4 y4 z4 where m3 = m4 , y3 = y4 , z4 = − z3 , so that I yz = 0 I zx = Σ ( I z′x′ + mz x ) = m1z1x1 + m2 z2 x2 = 0 continued COSMOS: Complete Online Solutions Manual Organization System From the solution to Problem 9.149 I x = 23.170 × 10−3 kg ⋅ m 2 I y = 21.444 × 10−3 kg ⋅ m 2 I z = 17.992 × 10−3 kg ⋅ m 2 λ OL = Now 1 ( −3i − 6 j + 2k ) 7 Have 0 0 I OL = I xλx2 + I yλ y2 + I z λz2 − 2I xy λxλ y − 2I yz λ yλz − 2I zxλz λx  Eq. ( 9.46 )  2 2 2   3  6 2 =  23.170  −  + 21.444  −  + 17.992    7  7 7   3  6   − 2 ( −5.1777 )  −  −   × 10−3 kg ⋅ m 2  7  7  = ( 4.2557 + 15.755 + 1.4687 + 3.8040 ) × 10−3 kg ⋅ m = 25.283 × 10−3 kg ⋅ m 2 or I OL = 25.3 × 10−3 kg ⋅ m 2