Well, my point still stands that it's a fist we're talking about here. Not a hammer. With a hammer, you're definitely right because you're mostly just lifting it over your head and letting it's momentum crush skulls. With a fist, momentum isn't involved. Again, punching a wall with my hand does about the same amount of damage to the wall (we're talking about a wall made out of that white stuff that's supposed to be made out of rocks and then covered in paper) as throwing a steel ball at it; yet my hand is much lighter than the ball. This is because I'm imparting the majority of my force with the fist less than a second before the impact, and exerting a constant force to keep it in motion, but throwing a steel ball imparts ALL of the force almost a second before the impact so air friction has an opportunity to slow it down before it impacts. Case in point, boxing gloves. Even though technically there's still a hand inside, there's a lot of fluff in between (and the idea is that the fist never directly imparts force to the opponent's face). If I were to throw a boxing glove at the wall with the same force as the steel ball, it would simply bounce off. But if I were wearing the glove on my fist and punched the wall, it would still damage the wall.
This is completely incorrect.
The reason why a boxing glove pads the impact is exactly the same reason why cars are designed to crush.
If you impart all of the force in one instant, even a tiny amount of momentum results in a gigantic amount of force. Its the change in velocity that is important. If you go to a stop instantly, slowing down from whatever speed you were at to a dead stop in as little time as possible you will be subjected to massive amounts of force.
If it takes longer to slow down the force will be far less.
With a fist, the bones of your knuckles are rigid enough that the fist stops almost instantly upon impact. Bone has very little give.
A boxing glove contacts the surface, and at the point of contact it begins transferring that energy. It takes longer for your fist to come to a complete stop because the glove is in the middle, and so while the same amount of force is transferred, it is transferred over a longer period of time and is thus mostly harmless.
If you are in a car and you floor it, you will feel pushed back in your seat. If you accelerate slowly you will feel much less force. The same is true for stopping. As they say, its not the fall that kills you, its the ground. In an impact the metal of the car will crush, much like a boxing glove, acting as a break so that your deceleration takes longer, so you are subjected to less force per unit of time.
Similarly, this is why guns are so dangerous. The recoil of a standard 9mm is very little. The impact of that same 9mm is also very small. But that small amount of force is concentrated into a tiny area, which is why it can pierce nearly anything. Your fists probably deliver far more energy than a 9mm bullet, but your fists do it over a much larger area. If you're holding a pointy object in your fist, like a screwdriver, then you do drastically more damage than with bare hands due to surface area.
/physics