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

2024
Views:

170

Pages:

2
Author:

palangresq3v

COSMOS: Complete Online Solutions Manual Organization System Chapter 9, Solution 154. m = ρV Have ( ) m1 = 2700 kg/m 3 ( 0.118 × 0.036 × 0.044 ) m 3 = 0.50466 kg Then 2 π  m2 = 2700 kg/m 3  ( 0.022 ) × 0.036  m 3 = 0.07389 kg 2  ( ) ( ) m3 = 2700 kg/m 3 ( 0.028 × 0.022 × 0.024 ) m 3 = 0.03992 kg Now observe that I x′y′ , I y′z ′ and I z′x′ are zero because of symmetry 4 × 0.022   x2 = −  0.118 +  m = −0.12734 m 3π   Now 0.022   y3 =  0.036 −  m = 0.025 m 2   m, kg x, m y, m z, m mx y kg ⋅ m 2 my z kg ⋅ m 2 mz x kg ⋅ m 2 1 0.50466 −0.059 0.018 0.022 −0.53595 × 10−3 0.19985 × 10 −3 −0.65505 × 10−3 2 0.07389 −0.12734 0.018 0.022 −0.16932 × 10−3 0.02926 × 10 −3 −0.20695 × 10 −3 3 0.03992 − 0.014 0.025 0.026 −0.01397 × 10−3 0.02594 × 10 −3 −0.01453 × 10 −3 continued COSMOS: Complete Online Solutions Manual Organization System And ( 0 I xy = Σ I x′y′ + mx y ( 0 I yz = Σ I y′z′ + my z 0 ) ) I zx = Σ ( I z′x′ + mx z ) Finally ( )1 + ( I xy )2 − ( I xy )3 = −0.6913 × 10−3 kg ⋅ m 2 I xy = I xy or I xy = −0.691 × 10−3 kg ⋅ m 2 ( )1 + ( I yz )2 − ( I yz )3 = 0.20317 × 10−3 kg ⋅ m 2 I yz = I yz or I yz = 0.203 × 10−3 kg ⋅ m 2 I zx = ( I zx )1 + ( I zx )2 − ( I zx )3 = −0.84747 × 10−3 kg ⋅ m 2 or I zx = −0.848 × 10−3 kg ⋅ m 2