1. Mechanical-Physical Nature of Friction Force and Coulomb's Law of Friction

Friction force, which acts in the direction opposing motion at the contact interface between two objects, is directly proportional to the normal force in accordance with Coulomb's law of friction by French physicist Coulomb, and is strictly divided into two states as follows:

• Maximum Static Friction (Fs_max): The threshold force required to initiate motion for an object at rest. Fs_max = μs × Fn
• Kinetic Friction (Fk): A constant resisting force when the object is already in relative motion and sliding. Generally, since the microscopic deformation of surface asperities decreases, the relationship μk < μs holds true. Fk = μk × Fn

2. Force Resolution Formulas on an Inclined Plane

The Newtonian mechanics vector resolution formulas acting on an object of mass m on an inclined plane tilted at an angle θ are as follows:

① Normal Force (Fn): The equilibrium component of gravity pushing perpendicular to the inclined plane.

F_n = m × g × cos(θ)  [N]

② Parallel Gravity Force (F_para): The effective component of gravity pulling the object down the slope.

F_para = m × g × sin(θ)  [N]

③ Slipping Point Condition: Slipping is triggered when the downward parallel driving force exceeds the maximum static friction limit.

F_para > Fs_max  ⇒  m·g·sinθ > μs·m·g·cosθ  ⇒  tan(θ) > μs

3. Acceleration and Friction Transition When Slipping Occurs

The instant the object exceeds the critical angle and begins to slide downward, the friction force abruptly drops from Fs_max to Fk. Due to this state transition, the object slides down the slope with a constant acceleration a given by:

a = g × (sin(θ) - μk × cos(θ))  [m/s^2]

This sudden static-to-kinetic friction transition is a key dynamic phenomenon causing non-linear vibration and failure behavior in mechanical systems, such as brake squeal, tectonic fault slip, and wheel slip.