Rolling Friction

Introduction

Friction is the resistive force that an object faces whenever it is facing a change in its state of motion. There are four types of friction: static, kinetic, rolling, and fluid which is also known as drag. 

When an object rolls on the floor, instead of being dragged or sliding, the rolling friction comes into play. It depends on the energy of deformation of the surface of the body and the energy of recovery of the surface of the body. 

In simpler terms, rolling friction takes place when a surface deforms due to rolling. The main cause of rolling friction is the dissipation of energy due to the deformation of the object. When the hardball rolls on a flat surface, it flattens out slightly at the point of contact as there are small bumps on the flat surface. While an object rolls, energy is generated.

In 1785, the physicist Coulomb published the first experimental study on rolling resistance.

The test used sharp rolling on an oak rail and an elm cylinder. The subsequent researchers improved his methods and results. However, some documents indicate that Leonardo da Vinci (1452-1519) was one of the first scholars to study friction systematically. He recognised the importance of friction in machine operation. He focused on various frictions, distinguishing sliding friction and rolling friction. 

Da Vinci proposed two elemental laws of friction, 200 years before Newton defined force. Da Vinci just said:

The contact area does not affect friction.

When the load on the object doubles, the frictional force also doubles.

Please pay heed to the fact that the first statement is not intuitive. Most of us assume that friction depends on the contact area.

Why Should We Study Rolling Friction?

To lessen the impact of friction, humans invented wheels. The effect of this innovation is everywhere in our day-to-day lives. Rolling an object is much easier than sliding it. Although moving wheels and rollers on a smooth plane involves much less dragging or friction than sliding from one flat surface to another, as smooth as it may be, it nonetheless proved that it is almost impossible to neglect friction. For example:

• A bike with a wide tire uses more fuel due to the increased rolling friction
• A ball rolled on grass gets less far than a ball rolled on a polished floor because it experiences more rolling friction

Understanding rolling friction helps us improve the quality of tires to minimise friction. Dealing with friction helps save fuel and make vehicles more economical and sustainable.

The Formula of Rolling Friction

Rolling friction is similar to kinetic friction. The only difference is that in rolling friction, instead of sliding, the object rolls on the surface in contact. Rolling friction is an important type of friction to understand because of the presence of many rolling objects around us like car wheels and windmills. 

Mathematically, it can be represented as

Fr = μrN

Where 

F is the magnitude of rolling friction,

N is the normal force on the object,

μr is the coefficient of rolling friction.

Impact and Causes of Rolling Friction

Rolling friction is a result of the energy dissipated in the process when one surface rolls over the other. When an object rolls on a surface, the following changes can be observed:

• The object deforms at the point of contact with the surface
• The surface deforms at the point of contact with the object
• The above changes create movement below the surface

(These changes might be non-observable with naked eyes)

What Causes the Above Changes to Happen?

The main reason for this friction is that the deformation energy is greater than the recovery energy. In addition to that, there is an adhesive force between the two surfaces that must always be overcome. The magnitude of friction depends on several factors, including:

• The sliding body quality
• The surface quality
• The load that the body applies on the surface
• The diameter of the rotating object

Coefficient of Rolling Friction

It is the ratio of the force of rolling friction to the weight of the object rolling.

μr = Fr / W …………. (N = W)

𝜇𝑠 is the static friction coefficient, 𝜇𝑘 is the kinetic friction coefficient, and 𝜇r is the coefficient of rolling friction.

𝜇𝑠 > 𝜇𝑘  >𝜇r

Laws of Rolling Friction

Now, let us understand the laws that govern this physics phenomenon.

When an object rolls on another object, the friction between the objects is called rolling friction.

The coefficient of rolling friction is

𝜇r = Fr / 𝑁. 

The Laws of Rolling Friction

1. For rolling friction (𝑓r), the response to a specific normal direction is not as important as static friction (𝑓𝑠) or dynamic friction (𝑓𝑘)
2. The rolling resistance is inversely proportional to the normal force
3. The contact surface is deformed for a short time due to rolling friction
4. Rolling friction depends on the contact area; therefore, if the tire’s (flat tire) air pressure is low, friction will increase
5. Rolling friction has a direct proportionality to the load or weight of the object and is inversely proportional to the radius of the rolling body. 

𝜇𝑟 ∝ w/𝑟

μr = Fr W 

μr = Fr mg

Conclusion

Rolling friction is a more defined category of friction. As mentioned above, it is similar to kinetic energy except the body is seen rolling here. 

From the above sections, we conclude that when an object rolls on a surface, rolling friction occurs due to the dissipation of energy that causes the surfaces to deform. If the object can overcome that deformation, it stays in motion. The coefficient of rolling friction has the least magnitude amongst static and kinetic friction coefficients for a body of the same weight in a similar environment. 

The coefficient of rolling friction varies according to the measure of the curvature of the rolling object, the weight of the object, and the force of the object.