COSMOS: Complete Online Solutions Manual Organization System
Chapter 9, Solution 194.
(a) Have
I AA′ = I GG′ + mra2
ra + rb = 290 mm
= 0.29 m
and
I BB′ = I GG′ + mrb2
(
I BB′ − I AA′ = m rb2 − ra2
Subtracting
( 41 − 78) g ⋅ m 2
)
= (2000 g) ( rb + ra )( rb − ra )
or
− 37 = (2000) (0.29) ( rb − ra )
or
ra − rb = 63.793 × 10−3 m
now
ra + rb = 0.29 m
so that
2ra = 0.35379 m
ra = 0.17689 m
or ra = 176.9 mm
I AA′ = I GG′ + mra2
(b) Have
Then
I GG′ = 78 g ⋅ m 2 − (2000 g) (0.17689 m) 2
= 15.420 g ⋅ m 2
Finally,
2
kGG
′ =
I GG′ 15.420 g ⋅ m 2
=
= 0.007710 m 2
m
2000 g
kGG′ = 0.08781 m
kGG′ = 87.8 mm
COSMOS Chapter 9 Solution 194
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