I also cannot download / watch the videos. Using Chrome 8.0.552.. and Firefox 3.6 @ Linux

http://ore.lefora.com/composition/attachment/3b2c8b50e1e3bb6b98f9057efa075f55/962123/Trident%20Physics%20Test%20Moth%20XC%201.m4v leads back to same page. Maybe spaces in filename... or one must be logged in to download?

I did a test with the trident type m and a behemoth and the trident does definitely spin. The math all seems correct, but it's hard to look at intetia tensors and know if they are correct.

The NPC tridents get spun around quite a bit too during docking/undocking by comparatively lighter ships. You won't notice it from one that's flying somewhere, but the ones that are parked like in a Small Skirmish seem to spin too much from something as small as a valk hitting them.

It almost seems like the mass of the ships is not being accounted for properly I believe its is usually a vector of the inertia and mass of both objects But thats kinda a math intensive method....

Yeah, the masses are being taken into account.
If you hit the trident with the same ship at the center of mass, the ship hardly moves.
If you hit it on its end, it starts rotating.
You can think of it as a sort of lever where the pivot point is the center of mass. As you get further away from the center of mass, less force is needed to rotate the ship.

I don't know if the inertia tensor is correct though, so that may be causing the seemingly large spin.
NPCs are able to better control ships in general, so seeing an NPC ship spin not as much/not at all is basically caused by the NPC compensating more quickly than a human can.

By the way, brakes only stop linear velocity, not angular velocity. There are no 'spin brakes'.

Then to move into suggestions, perhaps flight assist on a 0 m/s parked cappie engages some uber inertial dampening? (see "parking brake" request above)