This preview shows pages 1–2. Sign up to view the full content.
y
Each mass
mk
has a moment about
each axis.
)'
A twodimensional
array of masses
balances on its center of mass.
..
;
....
".
(~
U
"~~
''"'"
Masses Distributed over a Plane Region
Suppose we have a finite collection of masses located in the plane, with mass lIIi
nt the point
(x", y,,)
.
The mass of the system is
System mass:
A1
=
L
m".
Each mass "''' has a moment about each axis. Its moment about the xaxis is
and its moment about the yaxis is
",''x,,.
The moments of the entire system about
the two axes are
.
,
\
Moment about xaxis:
M.f
=
L
"''')'''
,
M).
=
L
III"X".
Moment about )'axis:
The xcoordinate of the system's center of mass is defined to be
_
My
L
11I".\',,*
x=
A1
=
'Llllk
.
With this choice of
x,
as in the onedimensional case, thc system balances about
the line
x
=
x.
The ycoordinate of the system's center of mass is derincd to be
 _
Mx
_ L
"'k)'''
y
.
M
Llllk
With this choice of )', the system balances about the line
y
=
)'
as well. The torques
exerted by .the masses about the line )'
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
 Fall '08
 Tyler/Ralston

Click to edit the document details