# Static friction

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## Definition

QUICK PHRASES: force that prevents surfaces in contact from slipping, force opposing slipping tendency for contact surfaces in rest, component along contact plane of contact force for contact surfaces in rest

### Intensional definition

Static friction is defined as the form of friction between two bodies, exerted via their surface of contact tangential to the surface of contact, when the surfaces of contact are not slipping against each other.

Note that this form of friction is acting not only when the two bodies are at rest with respect to each other, but also in the case of rolling -- when the bodies are moving relative to each other but there is no slipping at the region of contact.

### Tendency-based definition

Static friction is defined as the form of friction between two bodies that opposes the tendency for the surfaces of contact to slip relative to each other. In magnitude, it is equal to the net external force between the two bodies tangential to the surface of contact, and in direction it is opposite to that net external force.

## Model

According to the Coulomb model of friction, the maximum possible value of static friction is $\mu_sN$, where $N$ is the normal force between the two bodies and $\mu_s$ is the limiting coefficient of static friction. As long as the net external force parallel to the plane of contact has magnitude smaller than $\mu_sN$, there is no slippage and static friction acts. When the net external force exceeds this, slippage begins and static friction no longer applies.

## Caveats

Quick phrase for caveat Explanation Partial rescue
Actual value versus limiting value The value of static friction is not the same as $\mu_sN$ in general -- this is the limiting value or maximum possible value. The magnitude of static friction that acts when the surfaces are just about to slip against each other is indeed $\mu_sN$.
Relative rest versus absolute rest Static friction acts when the surfaces in contact are at rest relative to each other. Thus, if one box is placed on to of the other and the lower box is dragged such that the upper box moves along with it, then the form of friction that is operating is static friction, not kinetic friction. If one of the surfaces is fixed (for instance, it is a fixed floor or a very heavy object unlikely to move due to other constraints) then relative rest of the two surfaces is the same as absolute rest of the other surface.
Net horizontal force (elaboration of relative rest versus absolute rest) is adjusted to generate acceleration, not necessarily zero The magnitude of static friction is such that the net relative velocity, and hence, the net relative acceleration, of the two surfaces in contact is zero. When the two bodies are both at rest, this means that the net magnitude of force along the plane of contact is zero. However, if both bodies are accelerating in the same direction with the same magnitude, the net magnitude of force along the plane of contact must be such as to give rise to that acceleration by Newton's second law. If one of the surfaces is fixed (for instance, it is a fixed floor or a very heavy object unlikely to move due to other constraints) then relative acceleration of the two surfaces is the same as absolute acceleration on the other surface. Hence, in this case, if there is no slippage, the net relative acceleration is zero.
Body versus surface Static friction depends on the relative motion between the surfaces in contact, and not necessarily the bodies as a whole. Thus, it applies to the case of rolling but not to the case of pure rotation. When there is no change in orientation of the bodies (such as rolling or toppling), then slippage of surfaces is equivalent to relative motion of bodies. In particular, this applies in situations where we make the point mass approximation

## Confusion with Newton's third law

Newton's third law states that action and reaction are equal and opposite. In the simple case of two blocks with flat surfaces in contact where an external applied force on one block is exactly counterbalanced by a frictional force, the net acceleration of the blocks is zero. Thus, in this case, the frictional force exactly balances out the external applied force, and can be viewed as a response to the external force. However, this is not an action-reaction pair in the sense of Newton's third law. Rather, the friction forces that are exerted by the two surfaces of contact on each other form an action-reaction pair.

## Energy

Static friction does not result in any conversion of mechanical energy into other forms of energy. This is in contrast with kinetic friction.

## Related forces

### Other forms of friction

• Kinetic friction or dynamic friction is the friction between two bodies that occurs via surfaces of contact that are slipping against each other.

### Forces between rigid bodies

• Rolling friction: This is not really a form of friction, but rather, a normal force that effectively plays the role of friction due to local deformations of the surface.
• Normal force: The component of contact force in the direction perpendicular to the plane of contact.