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

2021
Views:

469

Pages:

2
Author:

Arielle Armstrong

COSMOS: Complete Online Solutions Manual Organization System Chapter 9, Solution 172. Mass of each leg is identical:  W /L  m= L  g  = 0.041 lb/ft (1.5 ft ) 32.2 ft/s 2 = 0.00190994 lb ⋅ s 2 /ft Also, I x′y′ = I y′z′ = I z′x′ = 0 for each leg, and x1 = x6 = 0 Now I xy = Σ I x′y′ + mx y = m2 x2 y2 + m3x3 y3 ( 0 y4 = y5 = y6 = 0 z1 = z2 = z3 = 0 ) ( ) = 0.00190994 lb ⋅ s 2 /ft ( 0.75 )(1.5 ) + (1.5 )( 0.75 )  ft 2 = 0.0042974 lb ⋅ ft ⋅ s 2 = 4.2974 × 10−3 lb ⋅ ft ⋅ s 2 I yz = 0 I zx = Σ ( I z′x′ + mz x ) = m4z4 x4 + m5z5 x5 ( ) = 0.00190994 lb ⋅ s 2 /ft ( 0.75 )(1.5 ) + (1.5 )( 0.75 )  ft 2 = 0.0042974 lb ⋅ ft ⋅ s 2 = 4.2974 × 10−3 lb ⋅ ft ⋅ s 2 continued COSMOS: Complete Online Solutions Manual Organization System I x = 14.32 × 10−3 lb ⋅ ft ⋅ s 2 From Problem 9.150 I y = I z = 18.62 × 10−3 lb ⋅ ft ⋅ s 2 λ OL = Now 1 ( −3i − 6 j + 2k ) and then 7 0  Eq. ( 9.46 )  I OL = I xλx2 + I y λ y2 + I z λz2 − 2I xy λxλ y − 2I yz λ y λz − 2I zxλz λx 2    3 =   14.32 × 10−3  −  + 18.62 × 10−3  7   ( ) ( )  −6 2  2 2    +    − 2 4.2974 × 10−3  7    7  ( )  − 73  −76   2  −3    − 2 4.2974 × 10−3      lb ⋅ ft ⋅ s 2  7  7    ( ) ( ) = 2.6302 × 10−3 + 15.20 × 10−3 − 3.1573 × 10−3 + 1.05242 × 10−3 lb ⋅ ft ⋅ s 2 = 15.725 × 10−3 lb ⋅ ft ⋅ s 2 or I OL = 15.73 × 10−3 lb ⋅ ft ⋅ s 2