If there are two bodies that have zero relative velocity, does that mean friction will not exist between them, since friction opposes relative motion. In the figure below i have two wheels A&B, with A rotating in clockwise sense and B in anti-clockwise sense. Suppose they are in contact at point p, then since linear velocity is tangent to the circle and in the direction of motion, therefore linear velocity at p will be in downwards direction for both A and B. Now, if the magnitude of their linear velocity is also same, then relative velocity of A with respect to B, will be zero at p. Will that mean frictional force on A(because of B) be zero at p?
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If the two surfaces are moving with the same velocity it means there will be no kinetic friction. There may well be a force of static friction acting between the wheels.
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$\begingroup$ So, static friction is applicable when two surfaces are actually at rest(with respect to some observer) and even when they are moving but have zero relative velocity(with respect to the same observer) . Am i right in saying that? $\endgroup$ Commented Apr 23, 2017 at 15:10
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$\begingroup$ That's right. Just look for sliding. If the two surfaces are sliding past each other you know it's kinetic friction. If they are not moving relative to each other then it's a static friction situation. $\endgroup$– M. EnnsCommented Apr 23, 2017 at 15:13
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$\begingroup$ @user47024 and M.Enns, there is one more detail to static friction. It is only present if the two surfaces would otherwise slide! Two objects touching and at rest relative to each other might and might not experience static friction (e.g. a book on a table) but if there also is a tension in the system that would cause them to move/slide over one another, then static friction must be present (like accelerating during a run; you slip on ice when there is not enough static friction, but not on asphalt). $\endgroup$– SteevenCommented Apr 23, 2017 at 15:55
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$\begingroup$ @Steeven : What would you say about the above situation, will there be static friction, if say wheel wheel A is rotated, such that the linear velocity at the point of contact between A and B is always same. Actually, i am studying friction wheels/ spur gears and have some confusion about the force analysis of these gears. $\endgroup$ Commented Apr 24, 2017 at 10:25
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1$\begingroup$ @user47024 As I commented, that depends on what would happen if one wheel wasn't there. Would there be a change in the velocity of the other? If so, then yes, static frictions prevents this change. Otherwise, no, there is no static friction. A book lying on a horizontal table experiences no static friction, but is the table a bit tilted and the book still remaining stationary, then there is static friction to prevent the sliding. Static friction prevents sliding if sliding wants to happen. $\endgroup$– SteevenCommented Apr 24, 2017 at 10:43