Consider an unsharpened pencil. With a little bit of work, it’s possible to get the pencil to stand on the flat, unsharpened end without tipping over. But what condition is needed in order for it to stay upright? It turns out that we need to focus on the center of mass. As long as the center of mass is above of the base of the pencil (the flat surface that it’s supposed to rest on), it will not fall over.

This gives us an explanation for some of our basic intuitions about objects and balance. Objects are harder to balance on a small base because the location of the center of mass only has a small area where it can be before it falls over. But objects with a wide base are more stable because the center of mass has a lot more room to move while still being inside the base. Furthermore, even if the object happens to roll a little bit, if the base is large, the object will fall back to the base instead of tipping over.

Items that are "top-heavy" fall over more easily, and this is due to geometry. When the center of mass is far from the base, a small change of angle can result in a large movement of the center of mass. This means that it’s easier for the object’s center of mass to go outside of the base, which makes it easier for it to fall over.

Internal stability is about maintaining the relationships between the different parts of the object. That stability is maintained by many forces.

When a rigid body is put under some sort of strain, there are internal forces that hold the object together to keep it from breaking. If the strain forces get too large, then the object will begin to warp and bend, and in some cases it will snap.

If there are two rigid bodies being held together, the forces used to hold them together are often through connecting pieces (like screws or nuts and bolts) or an adhesive. It is often helpful to use multiple connecting pieces to maintain the relationship between two bodies in order to resist having pieces rotate. An adhesive can be modeled as a lot of small connecting pieces, except that the connecting pieces are not nearly as strong

If there are more than two rigid bodies being held together, we can use other types of geometric concepts to help maintain the shape. Triangles are often used in construction because they resist changes to their shape. A shape like a rectangle can collapse in a process sometimes called parallelgramming.