I've been recently introduced to angular displacement, and I'm a little bit confused about it. I think that displacement which is a vector and which is defined as the shortest distance between any two points is different from angular displacement. Angular displacement is measured in radian or in other words it measures the 'angle' that a rotating body goes through. However, displacement vector is measured in meter. Angular displacement has the dimension of $1$; however, displacement vector has the dimension $L$. Is there any concept of the-shortest-distance-covered in angular displacement? I think angular displacement may just mean the change of position of a rotating body w.r.t. the angle subtended by the arc, traveled by it, at the center of the circle around which it is rotating.
If a body is rotating about the axis of a circle, and it moves from point A to B making an arc of length S, then the distance it covered is given by $S = θr$. However, the shortest distance it could have covered to reach point B can be given by the length of the vector D.