7.5 Center of Mass
In analyzing the collisions of two objects, the mass of each object before the
collision 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
may or may not be moving with the object(s)
may or may not be moving with the object(s).
Units?
[displacement] = [
m
]
F
l
l t’
I h
lid
h
f
Wh
i
th
t
f
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
spheres are separated by some distance
x
Where is the center
spheres are separated by some distance
.
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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