Angular displacement

In physics, Curvilinear motion is an unavoidable part. The motion of an object along a curved path is studied under circular motion or curvilinear motion. In the case of linear motion, the difference between the initial point and final point is termed as displacement. Thus the circular motion equivalence of displacement is Angular displacement. Represented using Greek letter θ. Measured using the unit degree or radian.

Angular Displacement Definition

Angular displacement is defined as “the angle in radians (degrees, revolutions) through which a point or line has been rotated in a specified sense about a specified axis”. It is the angle of the movement of a body in a circular path.

What Is Angular Displacement?

It is the angle made by a body while moving in a circular path. Before we go any further into the topic, we have to understand what is meant by rotational motion. When a rigid body is rotating about its own axis, the motion ceases to become a particle. It is so because in a circular path velocity and acceleration can change at any time. The rotation of rigid bodies or bodies which will remain constant throughout the duration of rotation, over a fixed axis is called rotational motion.

The angle made by the body from its point of rest at any point in the rotational motion is the angular displacement.


For example- If a dancer dancing around a pole does one full rotation, his or her angular rotation will be \(360^{o}\). On the other hand, he or she makes half a rotation; the displacement will be \(180^{o}\).

It is a vector quantity, which means that it has both magnitude and direction.

For example, an displacement of  \(360^{o}\), clockwise is very different from  \(360^{o}\), counter-clockwise.

Unit Of Angular Displacement

The unit for this is Radian or Degrees. Two pi radian equals to \(360^{o}\). The SI unit of displacent is meter. But the as angular displacement involves curvilinear motion. SI units of angular displacemnt is Radian or Degrees.

Measurement of Angular Displacement

It can be measured by using a simple formula. The formula is:

\(\theta =\frac{s}{r}\), where,

\(\theta\) is the angular displacement,

s is the distance travelled by the body, and

r is the radius of the circle along which it is moving.

In simpler words, the displacement of object is the distance travelled by it around the circumference of a circle divided by its radius.