The green table has a small rod that extends from its center of mass, hanging from which is a red plumb bob. When the table sits level, the plumb bob hangs above the center of its base. As you tilt the table as shown, the point above which the plumb bob hangs moves closer to the edge of the base that is still in contact with the surface of the demonstration table. As long as the plumb bob hangs within the area of the base, up to its line of contact with the surface, the table remains upright. As soon as the plumb bob moves past the line of contact of the table with the surface, however, the table tips over. A foam rubber block set where the top of the table will fall (not shown), cushions its fall and prevents damage.

The center of mass of an object is the weighted mean displacement of all of its mass points from some reference point, usually the origin of the coordinate system in which the object sits. This is the sum of the products of all the mass points with their distances from the origin, divided by the total mass of the object (r_cm = Σm_ir_i/M). If we set the center of mass of the object at the origin, we find that this sum equals zero. This tells us that, assuming that we could exert a force on the object at its center of mass, this would result in no torque on the object, but if we applied a force to the object at any other point, we would exert a torque on the object about its center of mass.

If the object is relatively small and close to the earth, then gravity acts uniformly on the object. That is, if the object is of uniform density, gravity exerts the same downward force on all of its mass points, and the sum of all of these forces is equal to a single downward force, F = Mg, acting at the center of mass of the object. The torque due to each of these forces, about the center of mass of the object, is τ = m_ir_i × g, and the sum of the torques is τ = (Σm_ir_i) × g. If we set the center of mass of the object at the origin, this sum equals zero. Thus if we apply a force at the center of mass that is equal to and opposite that of gravity, we can support the object without exerting a torque on it about its center of mass. This point at which the resultant force of gravity acts is also called the center of gravity. If we take the force of gravity as being uniform over the entire object, then the center of gravity and the center of mass are the same point. The green table shown above is not of uniform density, but it is symmetrical, and its center of mass (and center of gravity) is at a point within the vertical frame member along the line of the rod from which the plumb bob hangs.

When the table sits level, the demonstration table balances the force of gravity to support the weight of the table. The weight of the table is distributed over its base, at each point of which the demonstration table exerts an upward force to balance that of gravity. At any point not directly below the center of mass of the table, such a force should exert a torque about the center of mass, but each torque is balanced by an opposing torque from the corresponding point on the opposite side of the center of mass. Similarly, any torque that gravity could exert at the center of mass about any point on the base, is balanced by an opposing torque that it exerts at a corresponding point on the opposite side of the center of mass.

If you raise the right end of the base with the jack, as shown in the photograph, you exert a torque about the left end of the base. In doing this, you raise the center of mass and move the vertical line through it closer to the left edge of the base. Gravity exerts an opposing torque at the center of mass, about the left edge of the base, which keeps the table resting on the jack. As you continue to raise the right end of the base, you move the vertical line that passes through the center of mass closer and closer to the left edge of the base. This also decreases the moment that gravity has about the left edge of the base, and thus the torque that gravity can exert to keep the right end on the jack.

When you raise the right end of the table until the plumb bob hangs directly over the left edge of the base, the center of mass is now directly over the left edge of the base, and gravity cannot exert any torque about the left edge of the base. (See, for example, 28.18 -- Open door to demonstration preparation area, or 28.21 -- Positive and negative moments.) As soon as the plumb bob passes the left edge of the base, gravity now has a very small moment about the edge, and can thus exert a very small torque, which tips the table to the left. As soon as the table begins to tip to the left, and the center of mass passes further to the left of the edge of the table base, the moment that gravity has to exert a torque grows, and the table falls over.

The same thing would happen if you tilted the table in any other direction. When you tilt the table, as long as the vertical line that goes through the center of mass is within the area of the base of the table, gravity has a moment by which to exert a torque about the line of contact that returns the table to its upright position. Once the vertical line through the center of mass lies just outside the area of the base, gravity has a moment by which to exert a torque about the line of contact that causes the table to fall over.