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

2019
Views:

316

Pages:

2
Author:

hacedoras1kxy

COSMOS: Complete Online Solutions Manual Organization System Chapter 9, Solution 139. t = 2 mm ρ = 7850 kg/m3 Part : ( ) m1 = ρV = 7850 kg/m 3 ( 0.08 m )( 0.1 m )( 0.002 m ) = 0.1256 kg I x = I x + md 2 = 1 ( 0.1256 kg )( 0.08 m )2 + ( 0.1256 kg ) ( 0.1 m )2 + ( 0.04 m )2  12 ( ) = 66.99 × 10−6 + 1.457 × 10−3 kg ⋅ m 2 = 1.524 × 10 −3 kg ⋅ m 2 I y = I y + md 2 = 1 ( 0.1256 kg )( 0.1 m )2 + ( 0.1256 kg ) ( 0.05 m )2 + ( 0.1 m )2  12 ( ) = 0.1047 × 10−3 + 1.57 × 10−3 kg ⋅ m 2 = 1.675 × 10−3 kg ⋅ m 2 I z = I z + md 2 = 1 ( 0.1256 kg ) ( 0.1 m )2 + ( 0.08 m )2  + ( 0.1256 kg ) ( 0.05 m )2 + ( 0.04 m )2  12 ( ) = ρV = ( 7850 kg/m ) ( 0.2 m )( 0.2 m )( 0.002 m ) = 0.628 kg = 0.1717 × 10−3 + 0.515 × 10−3 kg ⋅ m 2 = 0.687 × 10−3 kg ⋅ m 2 Part : Ix = m2 3 1 1 ma 2 = ( 0.628 kg )( 0.2 m )2 = 2.093 × 10−3 kg ⋅ m 2 12 12 continued COSMOS: Complete Online Solutions Manual Organization System Iy = 1 1 m a2 + b2 = ( 0.628 kg ) ( 0.2 m )2 + ( 0.2 m )2  = 4.187 × 10−3 kg ⋅ m 2 12 12 Iz = 1 1 mb 2 = ( 0.628 kg )( 0.2 m )2 = 2.093 × 10−3 kg ⋅ m 2 12 12 ( ) Part : Same values as Part Total mass moment of inertia: ( ) ( ) ( ) I x = 2 1.524 × 10−3 kg ⋅ m 2 + 2.093 × 10−3 kg ⋅ m 2 I y = 2 1.675 × 10−3 kg ⋅ m 2 + 4.187 × 10−3 kg ⋅ m 2 I z = 2 0.687 × 10−3 kg ⋅ m 2 + 2.093 × 10−3 kg ⋅ m 2 I x = 5.14 × 10−3 kg ⋅ m 2 I y = 7.54 × 10−3 kg ⋅ m 2 I z = 3.47 × 10−3 kg ⋅ m 2