This preview shows page 1. Sign up to view the full content.
PROBLEM 9.110
Using Mohr’s circle, show that for any regular polygon (such as a
pentagon) (
a
) the moment of inertia with respect to every axis through the
centroid is the same, (
b
) the product of inertia with respect to every pair
of rectangular axes through the centroid is zero.
SOLUTION
Consider the regular pentagon shown, with centroidal axes
x
and
y
.
Because the
y
axis is an axis of symmetry, it follows that
0.
xy
I
=
Since
0,
xy
I
=
the
x
and
y
axes must be principal axes. Assuming
max
min
and
,
xy
I
II
I
==
the Mohr’s circle is then drawn as shown.
Now rotate the coordinate axes through an angle
α
as shown; the
resulting moments of inertia,
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