# why is very small angular displacement a vector quantity?How can we prove it?

Ganga sagar Kothashiv
32 Points
11 years ago

# Angular Displacement

Let us assume a giant wheel is moving, after some time, it will cover some distance.
We can see the change in position with respect to the initial point. We can calculate the change by studying the concept of angular speed.

## What is Angular Displacement?

We know that the Displacement is the shortest distance from the initial position to final position irrespective of the path taken by it to reach the final position.  It is the virtual straight line connecting initial position and the final position.

Here we can see the distance traveled (Actual Path) is AB + BC, but displacement is AC.
where, AC = AB + BC.
Now, What is Angular displacement?, In simple words we can say displacement covered in terms of angle.
Thus the displacement of the body moving in the curved path is represented by Angular displacement.
or
It is defined as the angle in radians through which a point has been rotated about a specified axis. It is the distance an object moves in a curved path. It is represented by the length of the arc of curved path.
The arc is measured in the angle and hence angular displacement is also measured as an angle.

## Angular Displacement Units

The Angular displacement is measured as angles and the angles are measured in radians. So, the unit of angular displacement is radians.

The angular displacement is represented in polar co-ordinates and not in x-y co-ordinates.

## Angular Displacement Formula

Let''s say, a body is moving in circular direction as shown in fig,

For $\theta$ angle and the radius of curved path is r. The linear displacement is related to the angular displacement as: S = r $\theta$ ...............(1)where r = radius of the curvature,
$\theta$ = angular displacement.
The equation (1) is the angular displacement equation.

BAYANA SAGAR
48 Points
11 years ago

# Angular Displacement

Let us assume a giant wheel is moving, after some time, it will cover some distance.
We can see the change in position with respect to the initial point. We can calculate the change by studying the concept of angular speed.

## What is Angular Displacement?

We know that the Displacement is the shortest distance from the initial position to final position irrespective of the path taken by it to reach the final position.  It is the virtual straight line connecting initial position and the final position.

Here we can see the distance traveled (Actual Path) is AB + BC, but displacement is AC.
where, AC = AB + BC.
Now, What is Angular displacement?, In simple words we can say displacement covered in terms of angle.
Thus the displacement of the body moving in the curved path is represented by Angular displacement.
or
It is defined as the angle in radians through which a point has been rotated about a specified axis. It is the distance an object moves in a curved path. It is represented by the length of the arc of curved path.
The arc is measured in the angle and hence angular displacement is also measured as an angle.

## Angular Displacement Units

The Angular displacement is measured as angles and the angles are measured in radians. So, the unit of angular displacement is radians.

The angular displacement is represented in polar co-ordinates and not in x-y co-ordinates.

## Angular Displacement Formula

Let''''s say, a body is moving in circular direction as shown in fig,

For $\theta$ angle and the radius of curved path is r. The linear displacement is related to the angular displacement as: S = r $\theta$ ...............(1)where r = radius of the curvature,
$\theta$ = angular displacement.
The equation (1) is the angular displacement equation.