Angular Displacement

Angular Displacement

Displacement is known as the change in the position of body or object with respect to a point of reference. Displacement is a scalar quantity. Similarly when an object or body changes both the position and angle then it’s displacement is calculated as angular displacement.
Angular-displacement is the change of the angle and the position of the body with respect to its initial position and angle.
Although displacement has magnitude and direction still it is a scalar quantity and not the vector quantity.

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Angular Displacement Formula

The angle of displacement is always measured in radians, since it is the change in the angle of the body with respect to its initial position.
The formula to find angle of displacement is given as;
Angular-Displacement = ???
Where,
??? = angle between the initial position of body to its final position.

How to Find Angular Displacement?

For finding angle of displacement, we need to follow these steps;
1. First obtain initial position of the body;
2. Obtain the final position of the body;
3. Find the angle between the two positions;
4. The angle is the measure of the angle of displacement.

In case if the linear displacement and the radius of curve is given then use the following equation to obtain the angle of displacement;
Angular-Displacement = ??? =
Where,
s = linear displacement; and
r = radius of curve through which the body rotates.

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Example of angular displacement:

A car is moving with the speed of 40 km/h on a curved surface having a diameter of 50 cms. Find the angle of displacement of the car along the curve at time t = 10 sec, 20 sec and 50 sec?
Solution:
As given in the question above we need to first identify the linear displacement at different time and then using the relation between the linear displacement and angle of displacement we will find the angle of displacement of the car at different times.
For time t = 10 sec;
s = 40 * (10 / 60 * 60) = 111.11 meters;
so the angle of displacement at time t = 10 sec is;
???t=10 = 111.11 / 0.5 = 222.22 radians

For time t = 20 sec;
s = 40 * (20 / 60 * 60) = 222.22 meters;
so the angle of displacement at time t = 20 sec is;
???t=20 = 222.22 / 0.5 = 444.44 radians

For time t = 50 sec;
s = 40 * (50 / 60 * 60) = 555.55 meters;
so the angle of displacement at time t = 50 sec is;
???t=50 = 555.55 / 0.5 = 1111.11 radians