2-18 - Announcements Midterm 2 is next week Thursday...

February 18, 2005
Announcements
• Midterm # 2 is next week!
Thursday, February 24th (Covers § 6.4 - 7.8)
• Start doing practice Midterms.
• Modification to Week 8 homework: Problems 1,
5, 7, 11, 12 and 15 in
§
8.3 are NOT part of the
assigned homework.
Today
•
§
8.3 Applications to Physics and Engineering:
Moments and Centers of Mass.
1

Consider a system of n particles with masses
m
1
, m
2
, · · · , m
n
located at points x
1
, x
2
, · · · , x
n
on the x -axis. The center of mass of the sys-
tem is located at
¯ x =
∑
n
i =1
m
i
x
i
∑
n
i =1
m
i
=
∑
n
i =1
m
i
x
i
m
,
where m =
n
i =1
m
i
is the total mass of the sys-
tem. The sum of the individual moments
M =
n
i =1
m
i
x
i
is called the moment of the system about
the origin . Note that
m ¯ x = M.

Consider a system of n particles with masses
m
1
, m
2
, · · · , m
n
located at points ( x
1
, y
1
), ( x
2
, y
2
) , · · · ,
( x
n
, y
n
). The moment of the system about
the y -axis is
M
y
=
n
i =1
m
i
x
i
,
and the moment of the system about the
x -axis is
M
x
=
n
i =1
m
i
y
i
.