Rolling FrictionIn general, a friction is a resistive force opposing a motion. The surface of contact plays an important roll on the motion of an object and the resistive force exerted on it. Before going into the details of what is rolling friction let us take a look at the types of frictions encountered when an object is in motion.

An object can be set into motion on a surface by different ways. The object may be pushed or pulled by a force such that only a particular surface is in contact with the mating surface on which it moves. In this case, the friction that resists the motion is called sliding friction. The another way is to make the object roll by placing it on circular wheels. In such a case, the friction gets reduced to a great extent, though, at the cost of additional weights of the carrier and its wheels. But, still a friction exists when the object is rolled on a surface. This type of friction is called Rolling Friction. 

Rolling Friction Definition

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A Rolling friction is a resistive force that opposes the rolling motion of an object. Rolling friction occurs when a round object rolls around a surface.One can obviously conclude by now that the study of rolling friction is limited to wheels or rollers and the surface on which they move. That is, for the same weight, the situation is same whether you put material A or material B on similar carriage and wheels.

In a broader study, the rolling friction depends on the nature of surfaces in contact. When a coach with steel wheel is pushed to roll on steel rails, it will travel much more distance than what a similar coach with rubber tires does when pushed with the same force on a road. The rolling friction in the first case is far lesser than in the case of the second.

Rolling Friction Formula

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When a rolling object like a wheel, roller or a ball rolls on a surface, generally the following phenomenon occurs:

1. A deformation of rolling object occurs at the mating area.2. A deformation of the surface occurs at the mating area. 3. The motion below the surface as a result of reasons 1 and 2.

The quantum of deformations in cases 1 and 2 depend on the nature of material of the object , surface and on the weight of the object.

Unlike the case of sliding friction, a formula for the force of rolling friction is not easily derivable for the reasons already explained. But empirically, the rolling friction formula can be given as,

Fr=urWwhere, Fr is the resistive force of rolling frictional forceur is a constant, called the coefficient of rolling friction for the given surfaces of contactW is the entire weight of the rolling object including the rolling mechanism

Most of us have used cycles and some of us still do. You must have noticed that well filled tyres make cycling a whole lot easier than the tyres that are not completely filled with air. This is due to rolling friction between the tyres and the road.

When a body rolls over another body, the places of contact get deformed and a slight bump is formed.

The bump caused in front has to be constantly overcome, Its like constantly climbing an incline. Secondly, the adhesive forces between the two surfaces also have to be overcome constantly. It is due to these two factors that rolling friction arises. It is denoted by fr and is given above.

Coefficient of Rolling Friction

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In the Empirical Formula for rolling friction, we mentioned a constant ur , called the coefficient of rolling friction for the given surfaces of contact. Coefficient of Rolling Friction is the ratio of the force of rolling friction to the total weight of the object. Since, it is a ratio of two forces, the coefficient of rolling friction is dimensionless and just a number.

The Coefficient of Friction purely depends on the set of surfaces involved in rolling. The values of coefficient can be found on empirical formulas established experimentally for case to case.For example, the coefficient of rolling friction in case of rolling of objects with iron wheels on steel rails is given by the following empirical formula.

ur = (0.005) (18d)12(100W)14

where, d is the diameter of the wheel and W is the total weight

Rolling Friction Examples

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The behavior of rolling friction is mostly based on case to case, let us describe some cases of rolling friction and explain their nature.

When the surface of the rolling object is soft because of the material or other physical consideration, then the surface of the object in contact gets deformed which results in increase in rolling friction because of addition of sliding friction due to such deformity. This is the reason why you find it hard to drive a bicycle with less air pressure in the tires.

When the surface is soft on which an object rolls, then there is a plowing action, i.e., the wheels spend some energy to clear the path. It leads to increase in resistive force, in other words, increase in over all rolling friction. This situation is experienced when you drive a vehicle on mud surfaces.

Surprisingly, when both surfaces are soft, the situation is better than the surface of the rolling object being soft. Because due to the deformity, the process of plowing is more easy and hence less energy is spent in that process.

The rolling friction has certain advantages as well. When the rolling of the objects stopped suddenly due to application of brakes, the rolling friction becomes a dynamic sliding friction which is advantageous from safety point of view. This is the reason, why trains running on steel rails requires a long braking distance compared to a car or a truck rolling on roads with pneumatic tires.