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2
2
00
bb
cm
zb
z
d
z
zd
z
z
bzdz
zdz
ρπ
==
∫
∫
∫
∫
2
3
cm
=
(e)
The center of mass is on the zaxis.
α
is the halfangle of the apex of the cone.
is the radius of
the base at
z
= 0 and
is radius of a circle at some arbitrary
z
in
a plane parallel to the base.
r
D
r
tan
rr
bbz
−
D
, a constant
()
2
22
tan
dv
r dz
b
z
dz
π
πα
−
23
11
tan
33
2
mr
ρ
ππρ
D
2
2
3
0
3
0
32
tan
3
2
1
tan
3
b
b
cm
zbz
d
z
b
b
πρ
−
−
∫
∫
z
b
z
z
d
z
+
4
cm
b
z
=
8.2
2
0
0
b
cm
b
cx dx
xdx
x
dx
cxdx
∫
∫
∫
∫
2
3
cm
b
x
=
8.3
The center of mass is on the zaxis. Consider the sphere with the cavity to be made
of a (i) solid sphere of radius
and mass
a
s
M
, with its center of
mass at
, and (ii) a solid sphere the size of the cavity, with
mass
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This note was uploaded on 01/06/2012 for the course PHYSICS 4360C taught by Professor Johnanderson during the Fall '11 term at UNF.
 Fall '11
 JohnAnderson
 Center Of Mass, Mass, Work

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