# Physics engine - collisions

I'm working on a 2D physics engine somulator and I want it to be very accurate on a Physics point of view. Currently I'm making some researchs about how rigid body collisions may be calculated, and I've found this page, that presents the following equation:

Where $w$ is the angular velocity, $j$ is the impulse during the collision, $r$ is the radius and $\hat{n}$ is (I'm not sure but I am guessing) a normalized vector.

My question is about what exacly is $I^{-1}$ .It says it's an inertia tensor, but for what I know it is used for 3D objects. Since my engine is 2D, may I simply use this formula:

Which is presented here as the moment of inertia of a rectangle. If yes, should I still use the (-1) power?

Btw, I would also accept a link to some pdf explaining how collisions change angular and linear momentum in 2D... this wikipedia page was the best I could find.

• I know it has been a while since this was asked, but according to Wikipedia( en.wikipedia.org/wiki/Moment_of_inertia ): "For bodies constrained to rotate in a plane, only their moment of inertia about an axis perpendicular to the plane, a scalar value, matters." in other words; if constrained to a 2D XY plane then the Inertia tensor 3x3 matrix can simply be replaced by the inertia about the axis of rotation. – Nikolaj Jun 11 '18 at 9:58

Yes the I must have the ^-1 exponent, otherwise the unit would not end up in $s^-1$ (the unit for angular velocity). $\hat n$ is the unit vector in the direction of exit after collision.