# angular displacement

Let’s see the figure above: in it there is represented a particle that describes a circular motion. The part of physics that deals with this type of motion is called **angular kinematics** . Let’s say that the particle, in circular motion of radius R and center O, moved from a point X to a point Y. In this way, we can say that the length *ΔS of the arc AB* is nothing more than the space traversed by the particle. Thus, we say that the **angular displacement** of the particle is the central angle *∆θ opposite the arc AB* . In such a way, we have:

**∆θ=angular displacement**

2a, below, we have that the displacement occurred in the **clockwise** direction , that is, in the same clockwise direction.

2b, below, the displacement from point P to point Q occurred in a counterclockwise direction, that is, in a counterclockwise direction.

*counterclockwise → ∆θ > 0*

*clockwise → ∆θ < 0*

As in trigonometry, we can also have angular displacements greater than one revolution. In the figure below, for example, we represent a situation in which a particle moved on a circle, starting from point A in a counterclockwise direction, and had an angular displacement greater than one turn, ending up at point B.