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5
8.5
Consider the sphere with the cavity to be made of a (i) solid sphere of radius
and and mass
a
s
M
, with its center of mass at
0
z
=
, and (ii) a solid sphere the size of the
cavity, with mass
c
M
−
and center of mass at
2
a
z
= −
.
The actual sphere with the cavity
has a mass
s
c
M
mM
=−
and center of mass
.
cm
z
3
33
44
7
4
28
3
sc
a
mM M
a
a
π
ρπ
ρ
=−=
−
=
8
7
s
M
m
=
and
1
7
c
M
m
=
From eqn.
8.3.2,
I
II
=
+
2
2
22
55
2
a
M
aM
I
=
+
2
21
3
1
57
4 7
0
a
I
ma
m
m
a
=− =
8.6
The moment of inertia about one of the straight edges is
2
z
I
Rd
v
=
∫
where
222
R
xy
=+
. From Appendix F …
2
sin
dv
r
dr d
d
θ
θφ
=
φ
θ
r
R
y
x
z
22222
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 Fall '11
 JohnAnderson
 Center Of Mass, Mass, Work

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