Mechanics

# 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.