Cfrtjryk

Momentum is defined by the product of mass and velocity. Now a projectile out of a gun has to have high velocity to penetrate a human body, as its mass isn't significant. But to reach this velocity, due to inertia/the law of energy conservation, momentum on both sides is to be equal. As there is strong negative acceleration in the opposite direction of the bullet, it should result in a strong force in the opposite direction of the bullet ($F = m*a $).

Therefore I wonder why shooting a bullet with a handgun is not ripping your hand apart.

Firstly, some guns do give quite a kick! So the effect you are thinking of is real.

However, conservation of momentum means that Mass_bullet * velocity_bullet = Mass_gun * velocity_gun. So the bullet's velocity is greater than that of the gun by a ratio of Mass_gun / Mass_bullet. Then energy is distributed in the same ratio because while energy scales as velocity squared, it also scales with the mass. So, it is useful for the gun to be heavy and/or for it to have a spring-loaded mechanism to slowly distribute the kick to your hand and body.

The handgun is braced with a large surface area of the hand, and the palm and entire hand are robust; the result is that the hand, or hand and arm, or hand and upper body are sharply displaced as a whole before the motion is damped by the rest of the body.

Some details of recoil are discussed here. The recoil of rifles, which are generally more powerful, braced near the shoulder, and operated near the face, can easily cause a broken collarbone, torn rotator cuff, black eye, and/or detached retina.

Thus, whether injury occurs depends on the stress induced in vivo from the acceleration of the brace position vs. the relative strength of the nearby organs.

Therefore I wonder why shooting a bullet with a handgun is not ripping your hand apart.

Because the mass of the handgun is greater than the mass of the bullet, and because the energy transferred from the gun to your hand is distributed across the surface of the pistol grip.

One of the more interesting things I heard on a trip to Williamsburg Virginia (which is period of ~1776; American Revolution) was the question of how much the muskets weighed. The historical figure answered (I don't recall the weight) and the questioner said in a surprised voice, "That's basically the same that guns weigh today!"

"Yes," replied this historical figure, "because the physics hasn't changed. They could make rifles lighter today, but they don't because the recoil would be worse."

There are other things put in modern pistols to reduce recoil like springs and discharge, but since you tagged it "Newtonian physics" I expect your are less interested in those things.