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Difference Between Translational and Rotational Motion

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Last updated date: 13th Apr 2024
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An Introduction to Motion: Entering the World of Mechanics

A change in a person's position with respect to time is referred to as motion. Any moving object can be seen with the naked eye by recognising the change in positional coordinates and then connecting it through the lens of an arbitrary observer. Both position vectors, such as displacement and distance, and speed factors, such as velocity, acceleration, speed, and time, can be used to describe motion.


When a body does not move in relation to time, we refer to it as being at rest. However, we refer to a body as being in motion when its position changes over time. Motion includes rotational, translational, periodic, and non-periodic motions and so a natural question arises: what is translational and rotational motion? This question is addressed in the following section.

What is Translation Motion?:

The movement of all points on a moving body in the same direction or line is known as translational motion. When an object is moving translationally, its orientation in relation to a fixed point remains constant. For instance, a racing car on the Monte Carlo race track, a man crossing the street, birds flying in the sky, and so forth.


Translational motion is often observable when the body moves in a straight line. A moving body moves when all of its points follow the same path or direction. When an object is in translational motion, its direction in relation to a fixed point remains unchanged.


In this type of motion, all points on the body are constantly experiencing the same magnitude and direction of accelerations and velocities. All of the points have the same trajectories. This implies that trajectories will coincide when placed one on top of the other. The body's orientation is essentially fixed in regard to one axis.


Rectilinear motion and curvilinear motion are two categories of translatory motion based on how an object moves. Rectilinear motion is the movement of an object in translatory motion in a straight line. A body is considered to be in translational motion when it is transferred or shifted from one location to another. An illustration of rectilinear motion is a car travelling in a straight line and a bullet being shot.The body/object in motion in these examples have all of their points pointing in the same direction. Whereas, in a curvilinear motion, it is the movement of an object along a curved route. In this kind of motion, a body or item moves along a predetermined or fixed arc. Motion in two or three dimensions is called curvilinear motion. A cricket ball high up in the air follows a projectile path which is nothing but a curvilinear motion.


Rotational Motion: 

A rotating object is one that travels in a circle along a fixed orbital path.


Dynamics of rotational motion shares every property with dynamics of linear or translational motion. The motion equations for linear motion share many similarities with the equations for the mechanics of rotating objects. Rotational motion only takes stiff bodies into account. A rigid body is a massed entity that maintains a rigid shape.


Rotation Around A Fixed Axis

The spinning body with a zero-velocity point around which the object rotates is seen in the figure below. This point may be anywhere—on the body or off—of the body. Since the axis of rotation is fixed, we only take into account the parts of the applied torques that are along this axis because only these parts cause the body to rotate. The perpendicular component of the torque usually causes the object's axis of rotation to veer away from its position. This causes some required constraining pressures to emerge, which eventually tend to cancel out the effects of these perpendicular components, preventing the axis from moving from its fixed location and causing its position to be maintained. The computation does not take into account the perpendicular components because they have no effect. For every rigid body rotating along a fixed axis, we need only consider the forces acting in planes perpendicular to the axis


A rotating body about its axis

A rotating body about its axis


Examples of Rotational Motion: 

Some instances of rotation about a fixed point include the rotation of a ceiling fan, the hour and minute hands of a clock, and the opening and closing of doors. Other examples may include the synergies of both linear(translational) motion and rotational motion about an axis of rotation such as Pushing a ball from an inclined plane is the best illustration of rotation about an axis of rotation. While the motion of the ball is occurring as it rotates about its axis, which is rotational motion, the ball reaches the bottom of the inclined plane through translational motion. The motion of the earth is another illustration of rotation about an axis of rotation.


Combined motion i.e., Translational and Rotational motion


Combined motion i.e., Translational and Rotational motion


Important Terms in Rotational Motion:

Moment of Inertia

The object's resistance to a change in rotation is gauged by its moment of inertia. I stands for moment inertia, which is expressed in kilograms per square metre (kg m-2). The following equations provide the moment of inertia:


$I = MR^{2}$, 


where R is the separation from the axis of rotation and M is the mass of the particle. The mass of the particle affects the moment of inertia; more the mass, more will be the moment of inertia.


Angular Momentum

The angular momentum L gauges how challenging it is to stop a rotating object. The following equation yields it:

 $L =\sum r\times P$


Torque

The twisting result of a force given to a rotating object at a distance r from its axis of rotation is known as torque. This relationship is denoted mathematically by the following:

$\tau =r\times F$


Differentiate Between Translational and Rotational Motion: 

S.No

Category

Translational Motion

Rotational Motion


Definition

The movement of all points on a moving body in the same direction or line is known as translational motion.

An object moving around on a fixed orbital path in a circle is said to be rotating.


Formula for acceleration

$a= \frac{\mathrm{d}v }{\mathrm{d} t}$

Where, a= acceleration

v= velocity

t= time

$a= \frac{\mathrm{d}\omega  }{\mathrm{d} t}$

Where, a= acceleration

$\omega$= angular velocity

t= time


Description of motion

Because translational motion is a linear motion, it can be described through two parameters i.e., distance and direction.

Because rotational motion is not a linear motion, it can be described through two parameters i.e., axis of rotation and angle of rotation.


Types of motion

This motion can be described in two types:

  • Rectilinear motion

  • Curvilinear motion

This motion can be described in two types:

  • Rotation around a Fixed Axis

  • Rotation about a fixed point


Property of acceleration

Acceleration may be uniform or non-uniform

Acceleration is generally non uniform(due to centripetal acceleration variable at every point of time)


Summary

The entire article may be summed up in a few key elements. Combining translational and rotational motion creates rolling motion. Rotational motion is a type of motion in which an object or body rotates around a fixed point, as opposed to translational motion, which is the movement of an object from one point to another. Combination motion refers to the movement of an object that combines two motions. Examples of combination motion include the way a cycle's wheels move, which mixes rectilinear and rotatory motion. The object's centre of mass or any other point in space could serve as the fixed point. The article explored what is translational and rotational motion.

FAQs on Difference Between Translational and Rotational Motion

1. What is translational and rotational motion?

In simple words, The movement of all points on a moving body in the same direction or line is known as translational motion. Whereas, An object moving around on a fixed orbital path in a circle is said to be in a rotational motion. Examples of translational motion include a moving car, moving train on tracks, etc. Examples of rotational motion include a revolving planet, spinning wheel about its axis ,etc.

2. What do you mean by motion?

A change in a person's position with respect to time is referred to as motion. Any moving object can be seen with the naked eye by recognising the change in positional coordinates and then connecting it through the lens of an arbitrary observer. Both position vectors, such as displacement and distance, and speed factors, such as velocity, acceleration, speed, and time, can be used to describe motion.

3. What is a basic distinction between translational motion and rotational motion?

When an object is travelling in a translational motion, its velocity remains constant. In contrast, when an object is rotating, the angular velocity of the object changes.

In rotational motion, an object's moment of inertia is taken into account as opposed to its mass when an object is moving in one direction.