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Take out the ruler, eraser, and pennies again. First, balance the ruler on the edge of the eraser. By our definition of center of gravity as "the point of balance," the center of gravity of the ruler must lie above the points of support provided by the edge of the eraser. The counterclockwise torque created by the weight of the ruler to the left of the eraser balances the clockwise torque created by the weight of the ruler to the right of the eraser. Now make two stacks of pennies with four pennies in each stack. Place one stack 1 in. to the left of the eraser and the other stack 1 in. to the right of the eraser so that the ruler remains balanced. The center of gravity of the pennies and the ruler is still above the eraser.
Now slide the right stack of pennies 1 in. to the right and move the eraser so that the ruler remains in equilibrium. Which way did you have to move the eraser? Which way did the center of gravity move? To keep the ruler in balance, you had to move the eraser to the right a little. The centers of gravity of the ruler and pennies also moved to the right.
Now move the right stack of pennies all the way to the right end of the ruler and move the eraser so that the ruler remains balanced. Again you had to move the eraser to the right, so the center of gravity of the system (ruler and pennies) moved to the right. You didn't have to move the eraser as far as you had to move the pennies, though. If some of the elemental parts of an object move or change position, the center of gravity of the object moves as well, although not as far.
Now take three pennies off the left stack and move the eraser so that the system remains in balance. You had to move the eraser to the right again, so the center of gravity moved to the right as well. If an elemental part of an object is removed from the object, the center of gravity of the object moves away from the point of removal.
Now add three pennies to the right stack and move the eraser so that the ruler remains balanced. The eraser is now farther to the right, and the center of gravity of the system has also moved farther to the right. If mass is added to an object, the center of gravity of the object moves toward the location of the added mass. Observe how many pennies are on either side of the center of gravity of the system now. The weights on either side of the center of gravity do not have to be equal; one penny does not equal seven pennies, but the torques created by these weights about the center of gravity must equal each other.
Once you feel comfortable with the concept of this exercise, please go to "Breaking Down the Exercise."
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