If you rotate from the waist, the pivot point is the center axis of your pelvis (whatever that means) and if the gun is tucked tightly into your shoulder and becomes part of you then how does the balance point of the gun affect your swing?
If you rotate from the waist, with the gun tucked tightly into the shoulder, as in shooting trap and skeet with the gun pre-mounted, balance has relatively little impact on swing dynamics. Balance is much more critical when the majority of the swing is incorporated into the mount from a low gun start. Shooting sporting and FITASC exclusively for a couple of decades, I was/am very critical of balance in those target guns preferring, as many do, to have the center of mass between the hands and a slight forward bias...slightly muzzle heavy rather than dead neutral. That compares pretty closely to my game guns as well.
Coming to trap late in life, I find I'm doing very well with a 9 lb gun that is extremely muzzle light....it balances well BEHIND the hinge. Adding a pound to the butt increased stability and reduced recoil while having negligible effect on barrel speed. I'd have a heck of a time trying to mount and swing it on a crossing target.
I am sure it is more complicated than a simple arc radius. Does the location of the concentration of mass of the gun change the feel?
Picture 2 4lb balls and a 4 foot broomstick. In total, they weigh 8 lbs. Attach the balls to extreme tips of the stick. The "gun" is 48" long and balances at 24". Move the balls in so they touch at the center. The 48" gun still weighs 8 lbs and balance at 24". Imagine how those 2 guns move about the center point. One muzzle is slow to start and stop, the other quick to start and with little momentum.
I am sure it does but don't understand how other than the apparently simple physics involved would explain it. If the gun is simply held tight to the body then the gun is not rotating but the body is with a wood and metal weight attached. Then the argument for a well balanced English gun makes no sense to me.
Well balanced English guns aren't normally used for American trap and skeet.
I would love to understand this better and I am sure others are also as confused as I am.
I am sensitive. No bashing please.
