What is rolling friction?

Short Answer:

Rolling friction is the resistance offered by a surface when a body rolls over it, such as a wheel, ball, or cylinder. It occurs due to the deformation of the surfaces in contact and the energy loss associated with that deformation. Rolling friction is usually much smaller than sliding friction, which is why wheels, rollers, and ball bearings are used in machines and vehicles to reduce energy loss. The magnitude of rolling friction depends on surface roughness, material properties, and the radius of the rolling object.

Detailed Explanation :

Rolling Friction

In Engineering Mechanics, friction is the force that resists relative motion between two surfaces in contact. When a body moves over a surface, it can do so in two ways — by sliding or rolling. If the body slides, the resistance offered is sliding friction. If it rolls, the resistance offered is rolling friction.

Rolling friction (also called rolling resistance) is the frictional force that resists the motion of a rolling object such as a wheel, ball, or cylinder on a surface. It acts at the point of contact between the rolling body and the surface, opposing the motion. Unlike sliding friction, which arises due to interlocking of surface irregularities, rolling friction mainly occurs because of surface deformation and energy loss due to compression of materials.

Definition

The rolling friction is defined as:
“The resistance force that acts at the point of contact between a rolling body and the surface, opposing its motion.”

It can also be defined as:
“The moment of resistance developed when a body rolls over a surface due to deformation of the rolling body and the surface.”

Mathematically, rolling friction can be expressed as:

where,

  • Fr = Force of rolling friction
  • M = Moment of resistance due to rolling
  • r = Radius of the rolling object

The coefficient of rolling friction (μr) is given by:

where h is the distance between the line of action of the normal reaction and the center of the rolling body.

Causes of Rolling Friction

Rolling friction arises mainly due to the deformation of the surfaces in contact. When a hard body like a wheel rolls over a surface, both the wheel and the surface deform slightly at the point of contact. The normal reaction does not act exactly through the center of the rolling body but slightly ahead of it, creating a resisting torque that opposes the rolling motion.

The major causes of rolling friction include:

  1. Deformation of Surfaces:
    • Both the rolling body and the surface deform under load. The reaction shifts forward, causing a resisting moment.
  2. Surface Roughness:
    • Uneven surfaces increase rolling resistance due to irregular deformation.
  3. Material Properties:
    • Softer materials deform more, leading to greater rolling friction.
  4. Internal Friction in the Material:
    • The energy required to recover from deformation (hysteresis) contributes to rolling resistance.
  5. Load and Radius:
    • Higher loads increase deformation, while larger radii reduce rolling friction.

Characteristics of Rolling Friction

  1. Rolling friction is much smaller than sliding friction.
    • Typically, rolling friction is 100 to 1000 times smaller than sliding friction.
  2. Depends on Deformation:
    • It arises mainly due to deformation and not due to surface interlocking.
  3. Proportional to Normal Load:
    • The rolling resistance increases with an increase in load acting on the rolling body.
  4. Depends on Radius:
    • Rolling friction decreases as the radius of the rolling body increases.
  5. Independent of Speed:
    • For moderate speeds, rolling friction remains almost constant.

Mathematical Expression for Rolling Friction

Let a wheel of radius r roll over a surface. Due to deformation, the normal reaction N acts at a small horizontal distance h from the center of the wheel.
The moment of rolling resistance is given by:

To maintain uniform motion, an external force F must overcome this moment. The force required is:

The ratio h/r is called the coefficient of rolling friction (μr), hence:

This shows that rolling friction is directly proportional to the normal reaction and the coefficient of rolling friction.

Comparison Between Rolling and Sliding Friction

  • Rolling friction is much less than sliding friction because there is no continuous surface contact or interlocking.
  • For example, pushing a heavy box directly on the floor requires a large force due to sliding friction, but placing the same box on rollers requires a much smaller force because rolling friction is minimal.

In numerical terms,

where,

  • = Coefficient of rolling friction
  • = Coefficient of kinetic (sliding) friction
  • = Coefficient of static friction

Examples of Rolling Friction

  1. A wheel rolling on a road:
    • The resistance a car tire faces while rolling is due to rolling friction.
  2. Ball bearings in machinery:
    • Bearings reduce sliding friction by converting it into rolling friction.
  3. Train wheels on tracks:
    • The steel wheels and rails have very low rolling resistance, improving efficiency.
  4. Conveyor rollers:
    • Reduce energy required to move materials in industries.
  5. Bicycle wheels:
    • Designed to minimize rolling resistance for smooth motion.

Factors Affecting Rolling Friction

  1. Material Hardness:
    • Hard materials deform less, resulting in less rolling friction.
  2. Surface Smoothness:
    • Smoother surfaces reduce resistance.
  3. Load on the Body:
    • Greater loads increase deformation and rolling friction.
  4. Radius of Rolling Body:
    • Larger radii reduce resistance by minimizing deformation.
  5. Speed of Motion:
    • Within limits, rolling friction remains constant; at very high speeds, it may increase slightly due to vibration or air drag.

Applications of Rolling Friction

  1. Transportation Systems:
    • Used in vehicles, trains, and bicycles to achieve efficient movement.
  2. Machinery Design:
    • Ball and roller bearings reduce energy losses in rotating parts.
  3. Material Handling:
    • Rollers and wheels allow easier movement of heavy loads.
  4. Industrial Equipment:
    • Used in conveyor systems for smooth operation.
  5. Aerospace and Robotics:
    • Reduces friction in rotating joints for precision movement.

Advantages of Rolling Friction

  • Reduces energy loss and wear.
  • Allows smooth and efficient motion.
  • Increases machine life and performance.
  • Enables easy movement of heavy loads.

Disadvantages

  • Still causes some energy loss due to deformation.
  • Rolling elements like bearings require maintenance.
  • Sensitive to load and surface conditions.

Practical Example

If a steel wheel of radius 0.5 m and normal load 1000 N has a rolling resistance of 0.002 (μr = 0.002):

Hence, only 2 N of force is required to keep the wheel rolling uniformly — much smaller than sliding friction for the same conditions.

Conclusion

In conclusion, rolling friction is the resistance that opposes the motion of a rolling object over a surface. It mainly arises due to deformation of the surfaces in contact rather than surface roughness. Rolling friction is significantly smaller than sliding friction, which is why wheels, rollers, and bearings are widely used in engineering to minimize energy loss. The magnitude of rolling friction depends on material properties, load, and radius of the rolling body. Understanding and minimizing rolling friction is essential for improving efficiency and performance in machines and transport systems.