Laws of Dry Friction and Coefficients of Friction 
 Magnitude of the maximum static friction force  
 Magnitude of the kinetic friction force 
symbol  description 
F_{m}  maximum force 
F_{k}  kinetic friction force 
μ_{s}  coefficient of static friction 
μ_{k}  coefficient of kinetic friction 
N  normal component of the reaction surface 
(Eq1) 

(Eq2) 

1.  No friction (P_{x} = 0)  F = 0 N = P + W  The forces applied to the body do not tend to move it along the surface of contact; there is not friction force.  
2.  No motion (P_{x} < F_{m})  F = P_{x} F < μ_{s}N N = P_{y} + W  The applied forces tend to move the body along the surface of contact but are not large enough to set it in motion. The friction force F which has developed can be found by solving the equations of equilibrium for the body. Since there is no evidence that F has reached its maximum value, the equation F_{m} = μ_{s}N cannot be used to determine the friction force.  
3.  Motion impending (P_{x} = F_{m})  F_{m} = P_{x} F_{m} = μ_{s}N N = P_{y} + W  The applied forces are such that the body is just about to slide, that is, motion is impending. The friction force F has reached its maximum value F_{m} and, together with the normal force N, balances the applied forces. Both the equations of equilibrium and the equation F_{m} = μ_{s}N can be used. Also note that the friction force has a sense opposite to the sense of impending motion.  
4.  Motion (P_{x} > F_{m})  F_{k} < P_{x} F_{k} = μ_{k}N N = P_{y} + W  The body is sliding under the action of the applied forces, and the equations of equilibrium do not apply any more. However, F is now equal to F_{k} and the equation F_{k} = μ_{k}N may be used. The sense of F_{k} is opposite to the sense of motion. 
Next Lesson: Angles of Friction⇒ 