# Direction Of Angular Displacement: 7 Important Facts

We will be describing 7 important facts related to the direction of angular displacement in this article. Whenever a particle is rotating around a particular axis, it will be displaced from one point to another. Angular displacement of that particle can be defined by this displacement of the particle. It depends upon the clockwise and anticlockwise direction of motion of the particle.

More specifically we can say that if we consider the figure 2 that is drawn below then to find the direction of angular displacement we have to notice the direction of the arrow that is drawn below. This arrow will tell us about the direction of angular displacement.

If the arrow is in the clockwise direction it means that the direction of angular displacement is downward and if the arrow is in the anti clockwise direction then the direction of angular displacement is upward.

## What is displacement in angular motion?

Displacement in the angular motion means angular displacement in rotational motion.

Angular motion is referred to as rotational motion. When a rigid body is rotating around a fixed axis then the angle subtended between its position of rest and its final position where it has reached after some time is known as the angular displacement of that rigid body.

Let us consider a rigid body which is at rest initially at point A. Suppose after time t it has moved to point B. Now if the angle subtended between the point A and the point B is θ then the angular displacement of that body is θ. Say at the point A the value of angle is θ₁ and the value of angle is θ₂ at the point B. so the angular displacement (Δθ) will be,

➡Δθ = θ₂ –  θ₁

θ₁ = 0, θ₂ =  θ

Therefore , ➡Δθ = θ₂ –  θ₁ = θ – 0 =  θ

The unit of angular displacement in the SI system is radian.

In simple words displacement in angular motion is the angular difference between two particular positions of a rigid body. The mathematical expression of angular displacement is,

Angular displacement = arc of the circle in which the body is moving/its radius

If the arc of the circle in which the body is moving is s and the radius of the circle is r,then angular displacement θ = s/r. As both s and r are angles and angular displacement is the ratio of these two quantities hence it is dimensionless.

Let us take an example. Say a rigid body is rotating around a circular path. One complete revolution by this rigid body will be equal to the circumference of the circular path. Circumference of that path is 2πr where r is the radius of that path.

Therefore s = 2πr and  θ = s/r = 2πr /r = 2π radian. It means that one revolution is equivalent to 2π radian.

## What is the direction of angular displacement?

The direction of angular displacement of a rigid body is always measured along the fixed axis around which it is rotating as it is an axial vector.

With the help of right hand rule we will be able to get a positive value for the direction of angular displacement. With the help of right hand thumb rule we can find the direction of angular displacement.

The direction of angular displacement is predicted by the direction of the thumb. Accordingly it will give the direction pointing upwards or pointing downwards.

## How to find the direction of angular displacement?

We will describe here how to find the direction of angular displacement.

Suppose a particle is moving around a fixed axis. According to the direction of motion of the particle we will be able to find out the direction of angular displacement. We will use the right hand thumb rule for this purpose as the thumb will indicate the direction of the angular displacement of that particle.

If the particle is moving in the anticlockwise direction then we will curl our fingers in the anticlockwise direction and then the direction of our thumb will point out the direction of angular displacement. As the thumb is pointing upwards in this case,hence the direction of the angular displacement is upwards. Figure 2 to show the direction of angular displacement when the direction of motion of the particle is anticlockwise

If the particle is moving in the clockwise direction then we will curl our fingers in the clockwise direction and then the direction of our thumb will point out the direction of angular displacement. As the thumb is pointing downwards in this case,hence the direction of the angular displacement is downwards. Figure 3 to show the direction of angular displacement when the direction of motion of the particle is clockwise

## Why is the direction of angular displacement perpendicular?

The direction of angular displacement is perpendicular to its plane. we will discuss why.

Suppose there are so many particles 1,2,3,4 ..that are rotating around a fixed axis. Now we have to find a quantity which is common for all these particles. If we notice we will see that the perpendicular of each of these particles are in the same direction as all of them are on the same plane.

Hence the direction of angular displacement of each of the particles will be the same i.e, in the perpendicular direction with respect to the plane of rotation.

We have seen earlier that according to the right hand thumb rule if the direction of motion of the particle is anticlockwise then direction of angular displacement is upwards and if the direction of motion of the particle is clockwise then direction of angular displacement is downwards. As the thumb is perpendicular to the plane of rotation hence the direction of angular displacement is perpendicular.

## Direction of angular displacement of earth

It is noticed from the north pole that the rotation of the earth is in the anticlockwise direction. It has been discussed earlier that when the direction of motion of a body is in anticlockwise direction then the direction of angular displacement will be upwards( right hand thumb rule). Therefore the direction of the angular displacement of the earth is upwards and it is perpendicular to its plane of rotation.

## Problem statements with solution

1. The earth rotates around the sun and completes one revolution every 24 hours. Now if the direction of the movement of the earth is in the anticlockwise direction what will be the direction of its angular displacement?

As the earth rotates  in the anticlockwise direction around the sun and completes one revolution every 24 hours,then according to the right hand thumb rule the direction of its angular displacement will be upwards and it will be perpendicular to the plane of rotation of the earth.

• A particle is moving around a circular path in the clockwise direction. What will be the direction of its angular displacement?