Stable and Unstable Equilibrium

Consider a block standing upright on a table (see Figure (a)). It experiences two forces: its weight, which acts from its center of mass, and the normal force from the table, which perfectly balances the weight. This block is in equilibrium, as we've discussed.

Now suppose we tilt the block to the right. The weight still points downward, and the normal force still points upward; both are equal in magnitude. But now there is only a single point of contact between the block and the table, and so the normal force must point there. The two forces don't align with each other, and so they will create a torque on the block; the block is no longer in equilibrium. However, if we think of the bottom point of the block as the pivot, we can see that the weight exerts a counterclockwise torque on the block, which will return it to its original equilibrium position.

But if we tilt the block a little farther to the right (Figure c), the weight now exerts a clockwise torque around the pivot, and the block will no longer return to its equilibrium position; instead it will tip over, into a new equilibrium position. (A handy rule of thumb for this situation is that the block will land on the side that is directly below the center of mass. For example, in (c) a line drawn straight down from the center of mass intersects the red side, and so the block will land on that side.)

States of equilibrium are often characterized as stable or unstable equilibrium depending on their ability to return to that equilibrium state after a small push (or other fluctuation). An extreme case is a coin balanced on its edge. Even if you can make them balance that way, a small vibration or breath of wind could be enough to cause them to follow over. A coin lying flat on the table, on the other hand, will not flip over without a major effort, and even if the coin is disturbed by bumping the table, it will return to its original state.

The demo below lets you play around with a block being tilted out of equilibrium. You might explore the following phenomena:

• See if you can balance the block on its corner. Where does the center of mass have to be for that to happen?
• See that a block with a lower center of mass tends to be more stable.
• See that a wider block is more stable than a skinnier block.