That's a perfect example, thank you.

>What I meant by “whipping a punch” was basically involving your shoulders in the punching motion. Snapping your shoulders like a whip as you’re extending your arm to punch seems to also give it more force.

The whole body should be involved, toes to knuckles. A proper punch or kick involves almost every muscle in the body, even the ones in the non-striking arm or leg. That's why proper technique has a twisting motion to the hips; you add the momentum of the entire upper body, not just the arm reaching out to strike. In my experience, setting the upper back solid when striking seems to make the biggest difference in the amount of force delivered as it provides a kind of backstop to the shoulder as the force of the strike is being transferred. If you don't keep your shoulders solid, and have good arm alignment when you strike, the force generated by your legs and hips goes into bending your wrist or shoulder instead of transferring into your target.

Wrist rotation is not 100% necessary; it's a technique I've encountered in some martial arts and ignored in others with no discernable difference in speed or power. I've personally had better results not rotating the wrist as I seem to have better alignment without rotation, but that may be a practice thing. It's also easier to get boxer fractures of the ring & pinky knuckle with a horizontal fist than it is with vertical or slightly angled fist. The slight gain of the twist (which is in itself debatable) is easily offset by having good alignment of the bones when striking.

In addition, that inertia isn't always a good thing on part of the person getting hit.

An often overlooked factor in how damaged you get is the amount of force it takes to overcome inertia. Hit a smaller person in the body, they go flying without breaking ribs because the amount of force necessary to knock them over is less than what's required to break ribs. Hit a bigger person, and their body has to soak more impact before movement occurs. Depending on the size difference and the amount of tissue padding the larger person has, there is a wide range of potential outcomes.

This combines unfavorably with the kinetic force equation, as velocity has more effect on force than mass. Smaller object moving faster = more penetration, which is bad for the person getting hit. It's far more likely to break ribs/jaws/orbitals/teeth as the smaller bits will fail before inertia is overcome.

Training helps with this, as you learn when to strike for maximum effect. It's counterintuitive due to the desire to avoid pain, but it's best to hit someone that is coming straight at you (who is usually swinging for your face) because you're adding their mass & velocity to your own. Hitting someone that's retreating reduces the force of your strikes. Think of the difference between a head-on collision and getting rear ended by someone going 50 when you're going 35.

For example: putting strong kicks into someone my size is usually less useful than putting them into someone larger than me. I have to time my kick so the person my size is advancing into the strike, giving me more force to overcome (and therefore more force I can put into them before they start changing direction) which directly translates into damage inflicted. With a larger opponent, I can deliver a full-force kick to the abdomen and they will fold like an omlette before they go flying because all the energy of my kick went straight into their body instead of getting wasted.