Welcome to PF!
So, I watched a decent fraction of the video and here's my impression:
William T said:
I watched this video and it seemed quite ludicrous to me. The man in the video measured sword speed (which I assumed was angular velocity) with mph.
He then continued to say that linear momentum applies when swinging a sword.
Presumably, you are suggesting that because there is rotation, linear speed and momentum do not apply. That's not entirely true and in addition the movement may be more complex than at first glance.
When swinging a sword, tennis racket, baseball bat or golf club, you combine multiple rotations and linear motions of different parts of your body. You rotate at the waist (hips), shoulders and wrists at the very least. Ultimately, though, the best results often occur if the tool is moving more linearly than rotationally as it hits what you are swinging at. In baseball, they call that "staying in the hitting zone". That comes from sliding your hips forward over your legs and shifting your weight from the back to the front leg. But either way, due to the multiple rotations the path of the tool tends to be straighter than you might think.
And even if it were true that you could model it as a pure rotation, you could still calculate the linear speed/momentum at the point of contact. Again, in baseball, this is how you differentiate between getting "jammed" and hitting further out on the barrel: the bat is moving at a higher linear speed further out, generating more power.
The bottom line, though, is that an object moving in a circle still has a linear speed -- or, rather, each point on the object has its own linear speed.
Last but not least, he expands on centrifugal force and gives an equation for centrifugal force, and uses it to debunk this science-fictitious sword. However, in my one community college physics class, I learned that centrifugal force is not a real force. I forget whether it's a combination of two forces, or just one force and a pre-existing velocity on the object.
We get this question about once a week and it is caused by introductory physics professors using a popular but misleading word choice to describe centrifugal force as "fictitious". It is called that because its source is reference frame dependent, but if you choose the rotating frame it is very much real. But even in the stationary frame, you just have to make sure you call it by the proper name in that frame: centripetal, not centrifugal (in one frame it points away from the center and in the other it points toward the center). There are some subtleties to it, but ultimately it is the same force: it has the same value whichever way you look at it.
If your general question is whether the video seems plausible? Yeah, it does to me. I didn't get to the end, but presumably he's trying to prove that no human could wield that sword usefully. I agree.