Whacked at the creche

The barrel keeps the shot channeled in the same direction meaning the momentum is higher.

Sawing off the barrel allows the shot to disperse widely, greatly decreasing the momentum of the shot - so shooting from a distance becomes inviable.
It does have the advantage of coverage at short distances, though.

This is not correct. The momentum of the shot is made up of the sum of the inertia of each pellet, focused in the one direction, these pellets carry a greater aggregate momentum in that direction however, their overall momentum is dependent on the initial force that is applied, i.e. the combustion force of gas behind the wad...

Secondly, it's arguable that because the pellets are not a classical bullet and therefore do not benefit in any meaningful sense from the phenomenon of rifling that there are in fact physical friction forces acting against the pellets on the exit from the barrel, therefore a shorter barrel would mean they exit with fractionally more momentum than should the barrel be longer...

It is correct to say that the net focused forward momentum is less with a shorter barrel because the pellets spread out in different vectors at an earlier stage, however there would be an increase in overall momentum as a sum of energy of each pellet free of it's directional vector...

Also, inviable is not a word...
 
This is not correct. The momentum of the shot is made up of the sum of the inertia of each pellet, focused in the one direction, these pellets carry a greater aggregate momentum in that direction however, their overall momentum is dependent on the initial force that is applied, i.e. the combustion force of gas behind the wad...

Secondly, it's arguable that because the pellets are not a classical bullet and therefore do not benefit in any meaningful sense from the phenomenon of rifling that there are in fact physical friction forces acting against the pellets on the exit from the barrel, therefore a shorter barrel would mean they exit with fractionally more momentum than should the barrel be longer...

It is correct to say that the net focused forward momentum is less with a shorter barrel because the pellets spread out in different vectors at an earlier stage, however there would be an increase in overall momentum as a sum of energy of each pellet free of it's directional vector...

Also, inviable is not a word...

Is is not, now?

Here la.

http://www.oxforddictionaries.com/definition/english/inviable

And I'll be back to school you on the rest later.
 
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