The idea is to calculate the momentum of the swing of a staff used in two hands ... move the fulcrum ... change the class of the lever ..

Can you describe what you want to do in general terms, rather than how you want to do it? Maybe something like "A player swings a staff and strikes an object. I want to know what damage the staff will do." The terms lever and fulcrum aren't really applicable to something being swung. Momentum is, indeed, mass*velocity, but mass*velocity*length aren't the right units for momentum.

It sounds (just a guess) like you may be interested in the force of the staff when it strikes an object.

A character attacks another, can he penetrate the other's armor, and how deep?

Okay. From your description it seemed it was something like that, but wanted to confirm.

[mvr] I thought that was the formula for angular momentum

That is the formula for angular momentum. You had mentioned momentum, levers, etc., and it didn't click in my brain. Angular momentum is related to a rotating object and its moment of inertia.

In any case, with regard to your questions regarding formulae - as mentioned in the guidelines in the Beginner's FAQ, the expectation is that you try to answer your question(s) yourself before posting. In this case, google is your friend, and, in general, much faster than posting a question and waiting a couple hours or even days for a response. Most, if not all, of the terms you asked about are "Google First Hits" - i.e., the first hit listed in the search results defined/described the terms quite nicely.

I guess I'm completely out of my depth here aren't I?

Yeah, it sounds like it. As your goal is to model armor damage from various impacts, and considering the terms you ask about to implement the actions, you should already have a good understanding of the physics involved, if not a good physics model setup for your characters. Alas, it appears you do not. E.g., you ask about formulas to calculate momentum in two situations, but there really is only one equation needed to describe a lever and fulcrum system. You also mention you would "like to calculate speed." Speed of what? Using what parameters? Those are rhetorical questions to help you understand that, at this point in the modeling you describe, that's like asking "How big is a box?"

I understand you want to add "realism" using principles of physics, even if in a limited way. Unless you already have a basic understanding of those principles, that's a bit difficult.

[ I want to ] determine the penetration of a blow against armor or flesh given contact area, the type of levering force, the angle of the blow, the distance the point of contact travels, the weight of the weapon, and the strength of the character. This is extremely complex, I know, so I'm looking for a happy medium of semi-realism

Considering the multitude of attributes you describe that you want to consider for the physics, the ship "Happy Medium" has sailed. I suggest you take just one of those parameters, and use a lookup table to determine a damage factor - e.g., strength-vs-damage-factor. Then, taking a much slower approach than you've described, refine the way you calculate the coefficients in that table by asking yourself questions such as "What causes 'damage'?" Speed at the end of the staff? Mass of the staff? ... Pick one of those answers, do a bit of research to understand how strength may relate to that parameter and work it into the equation for calculating the table entries.

That approach will force you [ pun intended ] to get a better understanding and familiarity with the physics involved in however you decide to model your characters.

You seem a bit fixated on momentum, fulcrums and levers to relate actions to damage. If you want to add "realism" in a "happy medium" between a simple lookup table and full blown physics modeling, that may be a difficult way to approach it. However, I'll attempt to provide you with some answers.

First: if you don't have a physics model for your characters, or at least a physics model for "swinging a staff," that must come first. It's a pretty big leap from "a character swings a staff" to a mathematical description of "how levers affect momentum." You'll have to describe (or provide a diagram of) the situation.

I could not find a formula for how levers affect momentum.

First: levers are discussed here. The equation possibly of interest is simply M1L1 = M2L2. N.B., 2 masses, 2 lever arms.

You will not be able to find a formula or equation for every situation you can think of. Solving problems usually results from the application of various principles of physics in combination. In general, the lever principle is rarely used to determine momentum or changes in momentum. Levers might be used to determine forces in some situations. I.e., momentum is mass * velocity, where velocity is a vector. For momentum to be changed, the mass, the direction of the velocity, the magnitude of the velocity, or a combination of those, must change. Further, momentum is a conserved quantity. When the momentum of an object changes, the momentum of one or more other objects must change by an equal and opposite amount.

With regard to "levers affecting momentum," if you provide a description (a diagram would be much better) for the situation you're thinking of, with indications of the 2 masses and 2 lever arms (i.e., where do you consider the fulcrum to be), what velocities are involved, etc., perhaps some help can be provided.

You probably want to find the impulse at the point of contact as well as the time to calculate damage (more time = biomass has time to displace, reducing damage)

Also area (the smaller area the impulse is distributed over, the more damage - sharp weapons)

So:

Impulse

Time

Area

Area is basically a weapon-specific constant (small for sharp weapons, big for blunt weapons), and time is how long it takes for weapon to stop after making contact (I dont know if time really matters - if it matters, the difference wont probably be too great - you could just apply some "reduction factor" between 0.5 (slow hammers etc) and 1.0 (swords/arrows etc) or something)

And more realistically those variables would vary over time (think a sword, it might at first have very small area but then it cuts deeper and area increases and force decreases over time - while for a hammer area is constant and force decreases)

So, how much impulse is at point of contact?

This depends on the point of contact, the velocity, the angular velocity, the mass, moment of inertia, whether the weapon stopped fully when hitting or continued movement after hitting etc.

So whats the velocity/angular velocity at point of contact?

Well that depends for how long a time the weapon was accelerated, how much force each hand applies (your fulcrum approach assumes the other hand applies no force and is static), where hands are placed, what path the weapon is moved (if you lift it up, it will take longer because of gravity and thus more energy will be 'charged' in the weapon), where it starts from (if you start holding the weapon high in the air, you get gravity potential energy as extra - if you start with weapon at ground, you lose overall energy due to lifting it more distance than lowering it)

And much of this is just raw data you have to provide (path of weapon, how much force hands apply....) so unless you actually intend to display everything visually, might as well skip some of the simulation and use numbers that make it feel correct.

Basically, it's where a character's hands push a staff in two directions at once.

The diagram you linked to is better approached as a system of torques producing angular acceleration, causing an increase in angular momentum over time. I.e., the two hands each apply a force at some distance from a center of rotation - producing torque. Similar to a linear system ( F = m*a ), T = I * a - where T is torque, I is the moment of inertia of the object, and a is angular acceleration. Given the length of time of the swing, determine the angular velocity, and from the angular velocity, the angular momentum. For a uniform staff (mass distributed evenly along the length), it looks like a decent I would be 1/3 m * L2 if the center of rotation is fairly close to one end of the staff.

As the hands move, the moment of inertia will change. You can look at the diagrams and estimate moments-of-inertia based on hand position - probably something between 1/3 and 1/12 m*L2