Friction fundamentals (dry sliding): What is the correct definition of the angle of friction between two contacting surfaces?

Introduction / Context:
The angle of friction is a geometric way to express the limiting friction condition between two dry, rough surfaces. It provides an equivalent angular measure of the coefficient of friction and is central to wedge, block-on-incline, and screw mechanics analyses.

Given Data / Assumptions:

• Surfaces are dry with Coulomb friction behavior.
• Impending motion (limiting friction) is considered for defining the angle.
• Normal reaction acts perpendicular to the contact surface; friction acts tangentially.

Concept / Approach:
At impending motion, friction reaches its limiting value F_lim = μ * N where μ is the coefficient of friction and N is the normal reaction. The vector sum of N and F_lim is the resultant R at the threshold of motion. The angle of friction φ is defined by tan φ = F_lim / N = μ. Thus φ is the angle between R and N at the limit state.

Step-by-Step Solution:

Verification / Alternative check:
On an inclined plane, impending slip occurs when W * sin θ = μ * W * cos θ giving tan θ = μ, hence θ = φ; the plane angle of repose equals the angle of friction, which confirms the definition.

Why Other Options Are Wrong:

• Ratio F/N is μ, not an angle; φ is the angle whose tangent is μ.
• “Force of friction when the body is in motion” defines kinetic friction, not the angle.
• “Magnitude of friction at the instant…” is again a force, not an angle.
• Angle between friction and surface is always 0 degrees by definition of tangential contact.

Common Pitfalls:
Confusing μ (a ratio) with φ (an angle), and mixing limiting (static) with kinetic friction.

Final Answer:
The angle between the normal reaction and the resultant of the normal reaction and the limiting friction