We measure coefficient of friction as the lateral force divided by normal force when two bodies slide against each other. But sliding is directional. Why not define it with respect to the directional vector also. Scientists who care about Watts per metre kelvin or Kilojoules per mol for other parameters didn't bother to define friction properly. Even in rotary conditions there is a tangent vector. Why this lack of care ?
From a mathematical point of view, the friction coefficient is an number that show the proportionality between the friction force and the normal force. Also, their representative vectors are mutually perpendicular, this is, we cant apply the scalar product or vectorial product to obtain the friction force from normal force.
Yes it is true that the friction varies with the direction, but I think it's not possible to represent that with an vector.
But really is an disturbing question!!!
To my opinion, friction is a two dimensional effect since the surfaces of both bodies may have some direction depended properties. This effects are coupeld by the limiting character of friction. One can observe different stability regions when adding a two-dimensional friction wrt. to one dimensional case to a dynamic system.
Best regards
Ch. Oertel
Padmanabhan, the vector characteristics is fulfill by concept of friction force. It looks like totally unnecessary to add another vector to do the same. But an nondimensional constant as the coefficient the friction represents has much more intersting aspects in terms of tribology. As a matter of fact, friction by itself has others pitfalls of interpretations much more challenger.
Regards, Toseli
To my opinion, friction is a property of any surface of matter, like gravity is for body with mass which we describe mathematically through gravitational force and gravitational constant. And nobody said why gravity doesn't have directional vector, because gravitational force is defining it i.e. vectorially. Likewise friction, frictional force and coefficient of friction is the mathematical representation of friction. And we know that gravity always attracts, in the same manner friction always oppose to motion when two bodies slide. Friction is the intrinsic behavior of surface of any bodies which has surface.
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