Angular Displacement – Mechanical Engineering

# Angular Displacement

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 360o. On the other hand, he or she makes half a rotation; the displacement will be 180o.

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

For example, an displacement of  360o, clockwise is very different from  360o, counter-clockwise.

### Unit Of Angular Displacement

The unit for this is Radian or Degrees. Two pi radian equals to 360o. The SI unit of displacement is meter. But the as angular displacement involves curvilinear motion. SI units of angular displacement is Radian or Degrees.

Measurement of Angular Displacement

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

,

θ 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.