Condensed-matter physics: Two bodies are better than one

Particles in a solid are tightly packed together (fixed shape) and often arranged in a regular pattern; in a liquid, they are close together with no regular arrangement (no fixed shape); in a gas, they are far apart with no regular arrangement (no fixed shape). Particles in a solid vibrate about fixed positions (cannot flow) and do not generally move in relation to one another; in a liquid, they move past each other (can flow) but remain in essentially constant contact; in a gas, they move...

Recall that a particle in equilibrium is one for which the external forces are balanced. Static equilibrium involves objects at rest, and dynamic equilibrium involves objects in motion without acceleration; but it is important to remember that these conditions are relative. For instance, an object may be at rest when viewed from one frame of reference, but that same object would appear to be in motion when viewed by someone moving at a constant velocity.
Newton's first law tells us about the...

The equilibrium of a two-force body is a particular case that is often encountered in practical applications. A two-force body is a rigid body that is subjected to only two external forces. For such a body to be in equilibrium, the two forces must have the same magnitude, the same line of action, and the opposite direction.

A composite body is a body made up of multiple parts, connected to form a larger, unified object. Each part has its own weight and center of gravity, which must be considered to determine the center of gravity of the composite body. In cases where the density or specific weight is constant, the center of gravity coincides with the centroid.
Composite bodies have widespread applications in mechanical engineering, from automobiles to aircraft to rockets. For example, an automobile wheel comprises...

When a force is applied parallel to the top surface of a solid, it resists the applied force due to the internal frictional forces between the layers of the solid known as shearing resistance. However, when the force is removed, the shearing forces restore the original shape of the solid. Other deformation forces also cause temporary changes in shape if the forces are not beyond a threshold magnitude. Solids tend to retain their shape, making the study of their rest and motion easier. Beyond...

Fluids differ from solids primarily in their molecular structure and stress response. Solids have tightly packed molecules with strong intermolecular forces, maintaining their shape and resisting deformation. In contrast, fluids have molecules spaced farther apart with weaker forces, allowing them to flow and deform easily.
Fluids, which include both liquids and gases, are substances that deform continuously under shearing stress. For example, water and oil are liquids with molecules that can...