It's not the centripetal force, but just where a straight line through the grip, perpendicular to the motion, lies in relation to (a) the centre of mass of the weapon, and (b) the point of contact with the target.
(a) If the line through the grip is forward of the centre of mass, then starting a swing will tend to align the weapon properly. No need to worry about it twisting in your grasp.
(b) If the line through the grip is forward of the point of contact, then the weapon will tend to stay aligned after contact. This is the same reason why bicycle stability depends on
"trail", and why trailers are stable when towed, but unstable when pushed.
In the picture, a straight sword chopping is a little unstable, for alignment, since it strikes a little forward of the line. A straight sword used to draw cut, where the grip leads in the cut, and a curved sword, have the point of contact (yellow circles) behind the line, and will be more stable.