Rigid Body Collision: Angular Velocity Question

[Jaevko]

So I'm upgrading my Physics Engine's Collision response system (don't worry, this is a pure physics question, no programming involved! Also don't worry about the time of collision, my collision detection system is separate and returns a time of collision for the response system to work with) and I found this really great guide: http://www.myphysicslab.com/collision.html

The equation I'm struggling with is Vap1 = Va1 + (ωa1 x rap)

Two questions:
1) The angular velocity is and has to be in radians/time_unit, correct? (Probably a stupid question, but I can't figure it out for sure and wanted to be certain). Or does it even matter as long as I'm consistent? Why?
2) How can you cross the angular velocity with the rap vector? Isn't the angular velocity a scalar? An example of how to accomplish the math would be greatly appreciated.

Thank you in advance for your time and help!

 

[Simon Bridge]

1. yes (radiens per sec). yes (it matters). (why?) because if you mess with the units you have to add in a scale factor to convert. (The equation uses the definition of "radians".)

2. Angular velocity is a pseudoector like torque. eg. picture a small mass moving in a circle anticlockwise with radius r and speed v.
At 12O'clock, the instantaneous velocity is to the left, the position vector points straight up, and the angular velocity (pseudo)vector points towards you. Notice how the relationship follows?

Also, in general, the 3D moment of inertia is a tensor.

 

[Jaevko]

Thank you for your reply; that was exactly what I was looking for!

 

[Simon Bridge]

No worries... happy hacking.