# B Vector equation of final angular velocities in a collision (graphics/physics engine)

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1. Dec 15, 2017

### cmcraes

Hi all! I'm currently working on a graphics/physics engine. The following Wikipedia page was extremely helpful in making rectilinear collisions look natural: https://en.wikipedia.org/wiki/Elastic_collision#Two-dimensional

Specifically, the very general vector form of the equation on the bottom of the page.

I know the equations of conservation of energy and angular momentum are analogous enough that there should be some angular equivalent of said formula in terms of moments of inertia and angular velocities, but when I input this analogy (all M's become I's and all v's become w's), this system doesn’t look realistic.

Is there an equation analogous to the one on the bottom of the above page which would provide me with realistic collision physics of rotating objects?

Thank you!

2. Dec 16, 2017

### kuruman

I think that just changing masses to moments of inertia and velocities to angular velocities is not enough. You are only conserving angular momentum about the center of mass but not of the center of mass. The total angular momentum of a spinning object of mass m as it moves with linear momentum $\vec{p}$ is given by $\vec{L}=I~\vec{\omega}+\vec{r}\times \vec{p}$. Here $\vec{r}$ is the position vector from an appropriate origin of the center of mass of each object. I would pick the point of contact. See if that fixes things for you.