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# Rolling Friction

## Friction

Friction, in general, is the resistance experienced by a body in motion on a surface or another body either also in motion or rest. Friction converts the kinetic energy of the bodies in motion to thermal energy, as demonstrated by rubbing two pieces of wood to create fire. Friction is a by-product of Newton’s third law of motion that states, “for every acting force, there is an equal and opposite reactive force”. The types of friction are:

• Dry friction: Occurs when two solid surfaces are in relative motion and contact. This is due to the irregularities in the surface of the bodies in motion. These irregularities are known as asperities. Dry friction is further classified into static friction (between non-moving surfaces) and kinetic friction (between surfaces in motion).
• Fluid friction: It is the friction found between the relative motion of two viscous fluids.
• Lubricated friction: It is the same as dry friction, but it is found in cases where there is a lubricating liquid between the contact of the two solid surfaces.
• Skin friction: The resisting force found between the motion of a fluid on a solid surface.
• Internal friction: It is found between the internal layers of a solid surface when it is undergoing deformation.

## Rolling Friction

Rolling friction, or rolling resistance/rolling drag as it is also called, is the kind of friction experienced by a body in a rolling motion on another surface. As opposed to sliding friction, where a particular side of an object is in contact with the surface throughout the duration of the motion, rolling friction is often much lower in magnitude compared to that of sliding friction.

## Laws of Rolling Friction

Three laws govern rolling friction, and they are:

Smoother the surface where the body is in motion, lower is the magnitude of rolling friction experienced by the body.

Rolling friction can be expressed as a product of load and constant to the fractional power. F = kLn

Rolling friction is directly proportional to the load and indirectly proportional to the body's radius in motion (i.e.) radius of curvature. F=μ×W/r

where

F = the resistive force of rolling resistance
μ = the coefficient of rolling resistance
k is a constant
W = the weight of the rolling body
r = the radius of curvature

## Causes of Rolling Friction

The rolling motion of a body is caused by the continuous deformation and recovery of the body in motion. For example, let us consider a tire rolling down a hill. When an external force pushes the tire, the point on the tire that touches the ground is temporarily deformed due to the resistive force exerted on that point by the ground. This compressed portion of the tire exerts a reactive force on the ground, pushing it forward. This cycle keeps repeating till the tire is stopped naturally or abruptly by an external force. The rubber in the tire experiences hysteresis and this hysteresis energy loss is dissipated in the form of heat. The energy of deformation is always greater than the energy of recovery, which is a characteristic of a deformable material.

## Hysteresis

It is defined as the dependence of the current state of a system on its previous (history) states of existence. In the example discussed above, the tire's motion is possible only if the tire had been compressed at an earlier moment, and because of that, it was able to exert a force on the ground. So the current state of the tire (either in motion/rest) depends on its history. But due to the resistive rolling friction experienced by the tire, during the continuous cycle of deformation and recovery, the tire will never be the same as at the start of a deformation cycle, meaning that due to non-elastic effects, the energy needed for complete recovery is never achieved even when the pressure is removed.

## Factors Influencing Rolling Friction

With time, any object in a rolling motion will eventually slow down due to friction. The most prevalent factors that influence the magnitude of rolling friction are the deformation of the rolling object, deformation of the surface, and movement below the surface (internal compressions), the diameter of the wheel, load on the wheel, surface adhesion, sliding, and relative micro-sliding between the surfaces of contact etc. Due to this factor of micro sliding, sand will offer higher rolling friction than a solid surface like concrete. And because the hysteresis losses predominantly depend on the nature of the material of the surfaces involved, a train car with steel wheels running on steel rails will cover a farther distance than a bus running on tarmac roads with rubber tires.

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