There's a really good example of the inertia thing you're talking about. Paquiao Vs Marquez 4 iirc where Paq gets knocked out. He's stepping into Marquez and moving directly into Marquez' hook and just gets obliterated. That hit was always going to be huge, but adding in Paquiao's own momentum is huge.

https://youtu.be/FNPmChbMsZQ

This is a good start to thinking about fight physics, another thing from physics that you have to think about while training are Newton's laws of motion. The third comes up a lot for a strike.

If two bodies exert forces on each other, these forces have the same magnitude but opposite directions.

So I need my body to be a wall at the moment of impact, any give in me is less force that they have to take. So if I throw a hook, and do it with just my arm, and my feet arent set, my core and ass arent fully engaged and/or my legs are wobbly, then Im going to move and that will lessen the impact on my opponent.

I'm not entirely sure what you mean by 'whipping' a punch. So I'll just go with what I know. There are 5 basic punches and the rest are just variations on them. Jab, Cross, Hook, uppercut, and overhand. Each of these punches is not just a different arm movement, but a different series of body movements. If we compare a jab and a weak side hook for example.

Jab: starts in the toes, and rear thigh, tensing those to give a rock solid base. Let the flex radiate upward to your core as you exhale sharply involving your abs and diaphram. Rotate your wrist as quickly as you can to unfold your arm straight out. You want your fist to impact at the exact moment that you fully clench your fist, the exhale completes and you flex your rear knee. Keep your center of balance directly under your shoulders the entire time, do not shift into putting more than 30% of your weight on your front leg. Your aim point should be about three inches behind the contact point. As soon as you make contact counter rotate your wrist to bring your arm back to your guard. This punch should be as fast and crisp as possible. You typically aren't looking for a knockout with a jab, you just want to take a small opening and wedge it open for a bigger punch.

Hook: From your back leg shift your weight from sode to side to your front leg. Load your front leg and prepare to drive back to the side that your weight just came from. This punch is all ass and obliques. Exhale sharply as you tilt your elbow to aim. Come across with your fist as hard and sharply as you can. Fully clench your fist and finish your exhale as you make contact. You want to drive this punch through something, I like to aim for putting the punch into the inside opposite wall of my opponents skull if I aim for the head and I want to drive it to the spine if I aim for the body. At the point of impact your entire body should be a wall of flexed muscle. Recover by twisting your elbow back into place for your guard.

In either punch you want to make an imaginary box, the top is your eyes, the bottom is your floating ribs, and the sides are the tips of your clavicle. This box extends out from your chest. Your hands do not leave this box. They are stuck in the box. We aren't getting fancy here, your hands stay in the box. And breathe dammit.

Allen key up top, wrench on the nut below. Maybe hit it with some WD-40 if you have access to it. Let that doak in for 15 minutes or so. Wear a leather glove especially on a hand pushing an allen key it wont dig into your skin and hurt so you can push on it harder. If you are having trouble getting in there take the wheel off to give yourself more room to work.