Rolling Motion

Rolling motion is an essential topic in physics. It is a combination of rotational and translational motion.

You must have seen an object, say a box, slithering down an inclined surface. At any given time, the box will have the same velocity. On the other hand, the movement of a ceiling fan represents rotational motion, where every particle of it moves in a circle. 

The rolling motion is a combined form of these two types of motion. Moreover, the ball’s motion during bowling or the snooker ball on a table are a few other rolling motion examples. 

In this article, you will understand the rolling motion definition in more detail, along with the equations related to it. 

An Overview of Rolling Motion

A rolling object simultaneously experiences rotating plus translational movement. Friction is necessary to rotate. 

‘Pure rolling’ refers to rolling motion without slippage. Here, the friction area between the wheel and the ground is in equilibrium with the latter, and no static friction force occurs when the wheels are in a rolling motion. 

When an object, like a wheel, seems to be in motion, its various components encounter various velocities. This aspect is the definition of rolling motion.

In physics, rolling motion without slipping is a combination of translation and rotation where the point of contact is at rest at any given instant. Therefore, you must first be thorough with pure translation and pure rotation to understand rolling motion. 

• Pure Translation: 

In this type of motion, the object’s velocity equals its centre of mass. It means all objects in pure translation have the same direction and speed and will move in a straight line if no external force is present.

• Pure Rotation: 

All the points of an object move at right angles to its radius in a pure rolling motion. Here, the speed of each rotating particle in the object is directly related to their distance from the rotational axis. The velocity of the object can be denoted by 

V = r * 𝛚

Here, 𝛚 = angular frequency. 

We know that r is 0 at the axis. Therefore, particles at the rotational axis don’t move at all. On the other hand, particles farthest to the rotational axis move at the highest speed.

Without Sliding, Rolling Movement

Rolling motion may occur without sliding. For example, consider the interaction between a car’s tyre and the roadway ground. The tyre spins when the driver lowers the car accelerator towards the ground, but the car does not move ahead due to mechanical friction between the wheels and the road. 

The tyre moves without slippage when the driver steadily accelerates the pedal, allowing the vehicle to move ahead. As the base of the tyre is at repose concerning the road surface, it implies a frictional force between the tyres and the road.

To understand rolling motion without sliding, we must first calculate the linear factors of speed and acceleration of that wheel’s centre of weight, considering the circular variables that characterise the wheel’s movement. 

Variables that Rotate

Let us look at variables that rotate.

• Rigid Structure: 

It is a concrete or embedded structure with all components intact.

• Rotational Axis: 

Each point on an object travels in a circular pattern with its centre around the rotational axis. During a specific time interval, each point rotates via a similar angle.

• Line of Reference: 

This factor is fixed within the object; it is parallel to the rotational axis and rotates along it.

• Angular Orientation: 

It is the angles of the standard line concerning the favourable direction of the x-axis.

Rigid Object Rotational Movement

As rotational movement is highly involved than linear movement, we mainly examine the rigid body movement. A rigid matter is an object with a firm weight and fixed shape, such as a phonograph disc. Several formulae based on the mechanics of spinning objects are related to linear movement equations.

Angular Speed and Angular Acceleration

The angles between the diameter at the beginning and end of a specific period are called angular dislocation of a revolving wheel. This angular acceleration acquires a similar shape as the linear acceleration.

Let us look at the kinematics formulae for rotating motion with continuous angular acceleration below.

Imagine a wheel moving in a single line without sliding. This wheel’s forward dislocation equals the linear dislocation of a spot positioned on the circle. The typical forward motion of the wheels in this situation is: 

v = d/t = (rθ)/ t = rω

Wherein r represents the length from the centre of circulation to the determined velocity spot. 

The speed is perpendicular to the route of the centre of rotation. This wheel’s typical forward speed seems to be a

T = r (ωf − ωo)/ t = rα

The element of acceleration appears tangential towards the centre of rotation. Thus, it reveals the object’s shifting velocity. The vector indicates a position similar to its velocity component.

If ‘ar’ be the radial acceleration, then: 

ar = v²/r = ω2r 

Conclusion

Rolling motion refers to the translational and rotational movements that occur without slipping. It is a typical combination of two types of motion we see every day in our daily lives. Ever since the invention of wheels, people have come across rolling motion. 

From the above article, you know that rolling motion without slipping consists of rotational and translational motion where the point of contact is at rest at a given instant. However, the point farthest from the point of contact moves at double the speed. 

Moreover, to gain insight into rolling motion, you must be thorough with angular speed and angular acceleration.