In this installment of the deep physics series, we’ll continue turning animations into salad by looking at the rotational dynamics in animations. As a note of warning to the reader. I will try to explain some physics in a clear manner, without equations, but there is an element of leaving the bike shed behind in this discussion.
We’ll refer back to our sword swings in Monday’s post as our starting point. The important thing to note is that swords do their fine work by turning rotational kinetic energy into entropy. We’ll discuss the role of the first two laws of thermodynamics in a later installment. But before we can deal with energy dissipation, we have to get to the point where we have that energy to dissipate. This means accelerating the sword through its swing arc.
Rotational kinetic energy is analogous to linear kinetic energy; with the moment of inertia standing in for mass and angular velocity standing in for linear velocity. Moment of inertia is a funny beast – and an extremely important one in the dynamics of mêlée weapons. Inertia is the predisposition for all objects to continue with their current state – i.e. resist change. Moment is a term for a bending/turning force. Thusly, moment of inertia is the predisposition of an object to resist changes in how fast it turns. Moment of inertia is composed of how heavy an object is and how that weight (mass really, strictly speaking “weight” is the force mass experiences under the influence of gravity) is distributed. If you were to hold a bucket of water in your hand and spin yourself in circles, you would find this much easier to do than if you were holding that bucket of water on the end of a ten foot pole. The latter had a higher moment of inertia, even if the mass is unchanged.
Another interesting thing about moment is, the more MoI that a rotating body has, the harder it is to stop; obviously. This means that it has a greater rotational kinetic energy and momentum of rotation; also known as angular momentum. This is of course why a maul head on the end of a 3 foot handle is so much more effective at splitting wood than one held directly in your hand. So the shape of a sword and how it is positioned determine how hard it is to swing, as well as how hard it hits.
So our sword moving through an arc hits something. We know this because the physics engine determined that the collision shape of the sword hit the collision shape of something else. We simply assume that the sword comes to a complete halt, or that it rebounds depending on the material that it strikes. Whatever momentum is lost translates to kinetic energy lost to entropy. This gives us a clear, consistent, measure of damage that is consistent and removes the need to have a “sword” entry in a weapon damage table. In fact, it relieves of the need for such a table at all for kinetic weapons. We simply track kinetic energy and changes.
In the next installment, we’ll review a methodology for tracking moment of inertia, angular velocity, momentum and kinetic energy.