Center of mass
The motion of a rotating ax thrown between two jugglers looks rather complicated, and very
different from the standard projectile motion discussed in Chapter 4. Experiments have shown
that one point of the ax follows a trajectory described by the standard equations of motion of a
projectile. This special point is called the center of mass of the ax.
The position of the center of mass of a system of two particles with mass m
1
and m
2
, located at
position x
1
and x
2
, respectively, is defined as
Since we are free to define our coordinate system in whatever way is convenient, we can define
the origin of our coordinate system to coincide with the left most object (see Figure 9.1). The
position of the center of mass is now
Figure 9.1. Position of the center of mass in 1 dimension.
This equation shows that the center of mass lies between the two masses, closest to the heavier
mass. In general, for a system with more than two particles, the position of the center of mass
will satisfy the following relation

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