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7.5 Center of Mass
In analyzing the collisions of two objects, the mass of each object before the
ollision is located at different points in space
collision is located at different points in space.
We define an average location
in space for the total mass of the system, whether
it be for 2 objects or
n
objects:
This location in space is called the
Center of Mass
of the system.
The Center of Mass
is a position relative to some fixed coordinate system, which
ay or may not be moving with the object(s)
may or may not be moving with the object(s).
Units?
[displacement] = [
m
]
For example, let’s say I have a solid sphere of mass
m
.
Where is the center of
mass of the sphere?
Clearly, it’s at the center of the sphere.
Now let’s say I have two spheres,
m
1
and
m
2
, where
m
2
=
m
1
.
The
pheres are separated by some distance
Where is the center
spheres are separated by some distance
x
.
Where is the center
of mass?
m
1
m
2
CM
x
x
CM
x
The center of mass is now located exactly between the two spheres.
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View Full Document Now let’s say I have two spheres,
m
1
and
m
2
, where
m
2
>
m
1
.
The spheres are
separated by some distance
x
.
Where is the center of mass?
M
m
1
m
2
x
x
CM
The CM is no longer exactly between the two masses, since more of the system’s
mass is located to the right, since
m
2
>
m
1
.
Thus, the CM lies closer to the mass on the right.
Note:
In the last two examples, the CM was not located within either object of the
ystem but was located out in space between them
system, but was located out in space between them.
Here we looked at just two objects, but we can generalize this to
n
objects.
The location of the CM of
n
objects is given by:
∑
=
=
n
n
i
i
i
x
m
x
1
CM
n
i
i
i
x
m
x
∑
=
=
⇒
1
CM
∑
=
i
i
m
1
tot
M
Example
:
A 5kg mass is located 2 m from the origin along the xaxis.
A 12kg mass is
located 10 m from the origin along the
x
axis.
What is the position of the CM of this
system?
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This note was uploaded on 08/04/2009 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.
 Fall '08
 SPRUNGER
 Physics, Center Of Mass, Mass

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