What describes the steepest angle at which loose material stays stationary without sliding?

The angle of repose is the correct choice because it specifically defines the steepest angle at which loose material, such as sand or gravel, can be piled without sliding down. This concept is fundamental in fields such as geology and civil engineering, as it describes the balance between gravitational forces acting on the material and the frictional forces that prevent it from sliding.

When loose materials are piled up, they form a slope. The angle of repose varies depending on the type and composition of the material, as well as other factors such as moisture content. At this angle, the forces acting on the particles are in equilibrium, which prevents movement; if the angle exceeds this threshold, the material will begin to slide due to gravity overcoming friction.

The angle of friction, while related, focuses more on the frictional force between two surfaces rather than the specific conditions of loose material. The angle of slope is a more general term that doesn't specifically address stationary loose materials. Inclination angle, similarly, refers to any angle of tilt or slope but lacks the context of stability under gravitational forces acting on granular materials. Thus, the angle of repose is uniquely suited to describe the condition where loose materials remain stationary.