COSMOS: Complete Online Solutions Manual Organization System
Chapter 9, Solution 114.
Mass = m = ρV = ρ tA
I mass = ρ tI area =
m
I area
A
(
Area = A = π r22 − π r12 = π r22 − r12
I AA′, area =
(a) I AA′, mass =
π
4
r24 −
π
4
r14 =
π
m
m
1
π 4
I AA′, area =
r − r14 = m r22 + r12
2
2 4 2
A
4
π r2 − r1
(b) By Symmetry:
Eq. ( 9.38 ) :
(
)
(
)
(
4
(r
4
2
)
− r14
)
)
I AA′ =
1
m r22 + r12
4
I CC ′ =
1
m r22 + r12
2
(
)
I BB′ = I AA′
I CC ′ = I AA′ + I BB′ = 2 I AA′
(
)
COSMOS Chapter 9 Solution 114
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