# Rolling Motion

## Introduction

The rolling motion refers to the combination of a type of translation motion as well as a rotational motion of an object. For example, in a machinery body, the rolling motion differs from the mass centre motion, which also signifies a type of translation motion of that particular body. During the time of the rolling motion of a machinery particle, the surface gets in close contact for a temporary period. During the rolling motion of a rigid body without slipping the particular object comprises the translational force, as well as rational motions during the surface contact, is instantaneously in the resting position.

## Types of rolling motion

The rolling motion comprises two different forms the Pure Translational Motion and Pure Rotational Motion. The pure translational form is the situation where an object moves at a velocity, which is equivalent to the centre of mass of that particular object.

$$\mathrm{V(r) = V_{center \:of \:mass}}$$

is the formula of this motion that can be calculated with the velocity of the object (Alehashem, Ni & Liu, 2021). According to this motion, an object moves along with a straight line if there is any kind of external forces are unavailable. Pure Rotational Motion is another type of motion with proper angles of radius according to the rotational axis of the objects.

## The properties of rolling motion

The velocity of the mass centre of the body mass can be denoted by $\mathrm{V_{cm}}$, which is also called the translational velocity. The geometric centre of the machinery body can be calculated with the symbol of C and the velocity is then signified with the symbol of Vr, which is perpendicular to the $\mathrm{CP_2}$ of this particular case. In the case of liner velocity, $\mathrm{V_r}$ is just opposite to the translational velocity symbolized by $\mathrm{V_{cm}}$. The radius of the wheel comprises the kinetic energy of rolling motion.

Figure 1: Rolling Motion expression

The measuring process of this motion will proceed with this formula V(r) = r * ω where ω denotes the angular frequency of the body when the r is zero in terms of the rotation axis that helps to gain the highest speed. Six different types of motion can be seen in a rolling object. Heave refers to a linear motion of the vertical z-axis, sway is a type of linear motion of the transverse Y-axis and the surge signifies the longitudinal x-axis while roll denotes the rotational motion that is seen around the transverse axis of the object (Skinner, Moss, & Hammond, 2020). The last one is yaw motion, which also a rotational motion is observed: around the vertical axis of the object. The rolling motion comprises rotational as well as translational kinetic energy. As per the requirement of the system, the rolling motion might also carry.

## The application of rolling motion

In daily life, different types of rolling objects can be seen like the rolling wheels of the car and bicycle. These are the most commonly seen movements in the day-to-day life. The rolling motion comprises two different types of motion or it is considered as the combination of two different motion types like translational as well as rotational motion (Yu, Jia & Geng, 2019). During the rolling notion of a machinery body, the lower surface came into a close contact that gets to deform in a temporary form of deformation.

Figure 2: The application of the rolling motion

This figure is an example of the motion of a rigid body. In this figure, the pure translational motion can be seen where P1 and P2 are the primary positions and the final position of the rigid and the triangular shape is the surface. The kinetic energy of the rigid body has a great impact on the rolling motion and this energy can be classified into two different categories translational as well as rotational kinetic energy

## The significance of rolling motion

The impact of the rolling motion of a rigid body movement is huge. During jumping or sliding the can be observed. In the making of the wheel and the application of car movement, the rolling motion has a great impact (Marques & Leite, 2022). The ceiling fan movement is also based on the application of rolling motion.

Figure 3: Velocity of the mass centre of a machinery body

## Conclusion

The translatory motion refers to rectilinear motion when the rigid body is in a translatory motion and proceeds with the straight line without any implication of any type of external force. The perfect example of this type of motion is a movement of a train on the railway track. The curvilinear motion denotes the movement of the car that moves along a curved surface. For example, during the time of the car turning the curvilinear motion is seen.

## FAQs

Q1. What is the moment of inertia in the rolling motion?

Ans. Rotational inertia is one of the most significant properties of rotating objects. The tendency of the rolling objects will remain a motion of rotation unless the application the torque. In the case of force is exerted the mass point maintains a distance from the pivot point and then the mass point gains the acceleration that is equivalent to F/m according to the force direction.

Q2. Does the rolling motion happens with slipping?

Ans. Rotational movement is another type of motion of the object that is commonly seen in car wheels and the movement of the earth around its own axis is also an example of rotational motion. The rotational velocity is commonly observed in the machinery body with a general angular velocity.

Q3. What is kinetic energy in the rolling motion?

Ans. In the pure rolling motion, the kinetic energy has a huge effect that can be presented with the formula $\mathrm{K\:=\:1/2\: I\omega^2}$. In the formula, I refer to the moment of inertia and ω stands for the angular velocity.

Q4. Which friction force affects the pure rolling motion?

Ans. In the pure rolling motion, mostly static friction is applicable. This friction between the surfaces of both pure rolling and rolling without slipping is also commonly seen.

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Updated on: 13-Oct-2022

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