Friction fundamentals — select the true relationship(s) among angle of friction, angle of repose, and coefficient of friction.

Introduction / Context:
Static friction at impending motion is characterized by an angle whose tangent is the coefficient of friction. For a body on a rough inclined plane, the critical inclination at which sliding starts—angle of repose—is numerically equal to the angle of friction. These relations are foundational in machine design and geotechnical slope stability analogies.

Given Data / Assumptions:

• Coulomb friction model with coefficient μ.
• Impending motion (limiting equilibrium).

Concept / Approach:

Define the angle of friction φ by tan φ = μ, arising from resultant reaction making angle φ with the normal at limiting friction. For a block on an incline, impending motion occurs when tan θr = μ, so θr (angle of repose) equals φ. Therefore, tan θr = μ and θr = φ hold together.

Step-by-Step Solution:

Verification / Alternative check:

Graphical friction circle or wedge analysis reproduces the same identities at limiting conditions.

Why Other Options Are Wrong:

“None” contradicts standard Coulomb relations; choosing any single statement would omit other equally true relations.

Common Pitfalls:

Confusing kinetic and static coefficients; applying relations away from the limiting state; mixing radians and degrees in computations.

Final Answer:

All the above.