This preview shows page 1. Sign up to view the full content.
PROBLEM 9.179
Consider a cube of mass
m
and side
a
. (
a
) Show that the ellipsoid of
inertia at the center of the cube is a sphere, and use this property to
determine the moment of inertia of the cube with respect to one of its
diagonals. (
b
) Show that the ellipsoid of inertia at one of the corners of
the cube is an ellipsoid of revolution, and determine the principal
moments of inertia of the cube at that point.
SOLUTION
(
a
)
At the center of the cube have (using Figure 9.28)
( )
22
2
11
12
6
xyz
I
II
m
a
a
m
a
===
+
=
Now observe that symmetry implies
0
xy
yz
zx
III
=
==
Using Equation (9.48), the equation of the ellipsoid of inertia is
111
1
666
ma
x
ma
y
ma
z
+
+=
or
()
222
2
2
6
x
yz
R
ma
++=
=
W
which is the equation of a sphere.
Since the ellipsoid of inertia is a sphere, the moment of inertia with
respect to any axis
OL
through the center
O
of the cube must always
be the same
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 07/11/2011 for the course EGM 2511 taught by Professor Jenkins during the Spring '08 term at University of Florida.
 Spring '08
 Jenkins
 Statics, Moment Of Inertia

Click to edit the document details