FYI, also modern helmets are not designed to stop bullets but rather to protect from shrapnel and hand grenades. Stopping a bullet would mean breaking the wearers neck. (The kinetic energy needs to go somewhere after all.)

Older steel helmets don't but modern IIIA-class helmets (e.g. ECH) do.

Kinetic energy is not a unsolvable problem, energy can be dissipated. The impulse is in fact the problem that can't be really worked-around (except spreading it over longer period of time) but the impulse of a bullet is low.

Level IIIA resists penetration from .357 SIG, 9 mm, and .44 magnum. Those are handgun rounds. It may stop some intermediate rounds if you’re lucky, but certainly not full power rifle rounds.

Helmets cannot deform as much as vests before seriously injuring the wearer, limiting their capacity to dissipate kinetic energy. And if you make them too rigid, concussion becomes a problem.

Deflecting it could maybe work though.

I don't think it would break the neck. Typical AK47 bullet at 100yd has momentum 5 kgm/s, which is about the same as a baseball at 77mph.

Guns are kinetic energy weapons, not momentum weapons. It’s the kinetic energy that matters.

Momentum is conserved, recoil momentum is the same as bullet momentum, yet recoil does not kill the shooter.

It's more the area of the bullet that matters. A small bullet or a thin needle require much less momentum/energy to penetrate a body than a big object.

If you place a bullet between rifle stock and the shoulder, then fire the rifle, it’s going to be mildly unpleasant, but the bullet won’t penetrate the skin, let alone kill the shooter.

Yes, but dissipating kinetic energy is a solvable problem unlike dissipating momentum.

The initial statement that's being refuted here is that a bulletproof helmet would break your neck and thus cannot work.

This statement is false because (besides such helmets existing on practice) your skull can absorb the momentum without too much damage and helmet can absorb the kinetic energy.

In the movies, the good guy casually fires a shot - one handed. He experiences almost no kickback.

But then the bullet hits the villain’s 300lb henchman, who is lifted off his feet and goes flying.

This is why people think bullets are magical momentum machines when in reality, due to air resistance, the momentum transfered to the target is even lower than at the moment of firing.

It indeed can't be too big because the shooter takes the same or greater momentum in the form of recoil. Conservation of momentum applies to the process of accelerating the bullet.

My favourite bit of AK47-helmet interface knowledge is that a French Jaguar pilot took an AK47 round to the helmet in the Gulf War. While flying.

(He survived, it's not really relevant here as it didn't stop the bullet - there was an exit hole too).

The bullet's kinetic energy is absorbed by the deformation and fragmentation of the projectile, the deformation of the helmet shell, the deformation/compression of rigid helmet pads, and conversion to heat.

The momentum of a projectile impact is very low, far lower than head contacts in sports. See, e.g.: https://i.ibb.co/7X6YCLD/ballistic-head-impact-updated.jpg -- from https://nap.nationalacademies.org/read/13390/chapter/9

If your helmet stops a bullet, there's some risk of head injury if the helmet shell, upon deformation, comes into contact with your skull. Otherwise you'll be okay. There's some historical information on this at: https://www.ade.pt/bulletproof-helmets

Also, the kinetic energy of a fragment near the site of an explosion can be higher than the kinetic energy load of a 9mm handgun bullet, which is generally the only small-arms threat that combat helmets are rated to stop.