Environmental Engineering Reference
In-Depth Information
10.10
sfasfd
(a) Show that the moment of inertia tensor of a uniform solid right circular
cone about its apex is given by
5
m
R
2
h
2
3
+
0
0
4
5
m
R
2
h
2
=
I
3
0
+
0
4
3
10
mR
2
0
0
where
m
is the mass of the cone,
R
is the radius of the base,
h
is the
height and the symmetry axis lies along
e
3
.
(b) A solid right circular cone rolls on its side without slipping on a hori-
zontal surface. The cone returns periodically to its starting position with
constant angular speed
ω
. Show that the kinetic energy of the cone is
given by
6
h
2
.
3
mω
2
h
2
40
R
2
+
T
=
h
2
+
R
2
