Moment at a point in a beam

I have a doubt Applying moment at a point in a beam. Normally in beam theory we define moment at a point about some coordinate system.Does it mean that the point will try to accelerate around some axis in that coordinate system? The path of the point will be in a circle with centre at the coordinate system and radius as the distance between the coordinate system and the point in the beam.

if we define the moment about the coordinate system at the same point itself what will be the result?

HallsofIvy