The shorter barrel would only reduce the time over which the recoil force acts, the recoil force itself would be the same. Yes it is true that the mass of the projectile would have to include the mass of the propellant (which is the same as the mass of the propellant gas due to the principle of conservation of mass), but with the mass of the gun being reduced, the recoil acceleration would be increased.
You are wrong about the muzzle brake. The point of a muzzle brake is to utilise the propellant gases and push them backwards after the projectile exits, hence counter-acting the recoil force. This would not apply to a sawn-off weapon, as the gas pressure would continue to exert force forward, causing the equal and opposite force backwards. Certain muzzle brakes (like the cutts compensator on the Thompson, actually push these gases up to counteract the weapons tendancy to rise.
Rob
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