117-120] LAWS OF FRICTION. 115 



Each of the bodies is regarded as having a particle at P. 



The particle of A at P will have a certain velocity, and 

 similarly for the particle of B at P. The velocity of the particle 

 of A at P, relative to axes parallel to the axes of reference drawn 

 through the particle of B at P, is the relative velocity of the 

 points in contact considered as the velocity of a point of A 

 relative to B. In like manner there is an equal and opposite 

 relative velocity of the points in contact considered as the velocity 

 of a point of B relative to A. 



The condition of contact is that the relative velocity just 

 described is localised in a line in the tangent plane at P, or that 

 the resolved part of this velocity in the direction of the common 

 normal vanishes. 



The first law of Friction is that the friction on \ n [ at P is 



opposite in sense to the relative velocity of the points in contact 



considered as the velocity of a point of ! D ! relative to \ . 



(B) (A 



The second law of Friction is that the friction F and the 

 pressure R are connected by a relation of inequality F ^ pR, 

 where //, is a constant depending only on the materials of which 

 the bodies are composed. The constant JJL is called the coefficient 

 of friction. 



When the relative velocity above described is zero, the motion 

 is described as rolling. In order that rolling may take place it is 

 generally necessary that the coefficient of friction should exceed a 

 certain number depending on the circumstances of the case. A 

 motion of two bodies in contact which is not one of pure rolling is 

 described as a motion of sliding or slipping. The rule for the 

 direction of friction may be stated in the form that friction tends 

 to prevent slipping. When slipping takes place F pR When 

 the bodies are sufficiently rough to prevent slipping throughout 

 the motion they are sometimes said to be perfectly rough. 



120. Resistances. Friction belongs to a class of forces 

 known as resistances. The characteristics of a resistance are that 

 it acts on a particle in the direction of its velocity relative to 

 some frame (not necessarily the frame of reference) in the opposite 

 sense to this velocity. 



82 



