There are several important factors which relate to muzzle rise. They can probably be divided in to two torque forces:

• Bore Axis over Center of Gravity, and the Moment of Inertia. If the bore is directly in line with the center of gravity, there is no torque when fired, and the firearm is propelled directly backwards with no muzzle rise. This isnt usually the case, and even if it was, CoG would change as the magazine depletes. So the angular velocity or muzzle rise of the firearm is the distance above the CoG the bore is, multiplied by the moment of inertia. Moment of inertia is the distribution of mass away from the CoG. On firearms, a muzzle brake, brass/steel magwell, frame-weight, flashlight, or compensator will add mass at an extreme end of the firearm far away from the CoG, this greatly increases the Moment of inertia. Like swinging a hammer by the head instead of the handle.

• Bore axis above the center of rotation of the shooter. The firearm is not freely floating in zero gravity, but is instead being gripped by you. The recoil impulse could be directed perfectly rearward, but this force will ultimately be absorbed by the shooter's hands, wrists, shoulder, abdomen, and legs. With a pistol, the bore is always above your hands and wrists, and the recoil will always try to rotate the shooter's hands, wrists, and arms upwards due to the resulting torque. With a rifle, the vector of the recoil force is imparted on the shoulder. If the bore us above the center of the shoulder pad, the rifle will rotate upwards when fired. Even if all other torque are neutralized, the force is pushing rearwards on the upper body of the shooter, and this force is trying to tip the shooter over backwards or their feet.