Center of Mass

The  pictures below show the same scale in different static equilibria situations. 
Pay attention to the Forces acting on this type of lever.  What class of  lever is it?  Why?

In the first picture the "weight" is moved to the right hand side of the beam.  As you can see, the components of the vertical forces are quite different than in the second scale (ΣF_y= 0 and ΣF_x= 0 -- In each of the two cases, both conditions for static equilibrium are satisfied).  If we wanted to bring the beam back to the "zero" point on the balance we would have to add more masses to the pan. In the second balance the "weight" is moved closer to the fulcrum.  This allows the beam to assume a horizontal position.
In the second scale the "weight" is placed at the center of mass of the beam so that the force in the vertical direction (F_N) is balanced against the force of gravity.

Also notice the role of Torques in  each of the two balances.  The position of the weight along  the lever arm (the beam) determines the amount of  torque .

The above example illustrates that for any given object, the force of gravity can be considered to act upon a single point.  This point is called the center of mass and sometimes it is also referred to as the center of gravity.

The force of gravity, as we know, acts on all parts of an object.  In Physics we place the force of gravity at the center of mass of the object in question. This helps us to draw free body diagrams and analyze the motion of the object.  Regularly shaped objects and regular geometric figures have their center of mass placed at the geometric center.  For other irregular objects we can use the concept of Torque to find the location of the center of mass (or the center of gravity -- which ever is appropriate)..

  Read About Center of Gravity

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