# How calculate the total energy of a collision?

Hello guys,

I am developing a physics system that simulates collision between two cubes. I need to calculate the total energy in those cubes in an instant before the collision. I know that the total kinetic energy in this case is the sum of the angular velocity energy and the linear velocity energy:

E = 1/2 * m * v² + 1/2 * I * w²

My question is, in the energy from angular velocity, "I" is the module of the components (Ix, Iy, Iz) of the inertia, right? Or I need to do some cross product before?

Thanks

## Answers and Replies

i think do this is more helpful
calculate energy about com and energy of com wrt ground

DEvens
Education Advisor
Gold Member
https://en.wikipedia.org/wiki/Moment_of_inertia

Colliding cubes is tough. To get it accurately in 3-D you would need to work out the exact collision of the cubes. To get that you will need to know the relative velocities, angular velocities, and masses.Then you have to work out what it does to the linear and angular momentum.

As Shreyas suggests, the centre of momentum frame will get you a good start. In that frame you have each cube with linear momentum of equal magnitude, but exactly opposite direction. After the collision they are still "back to back" w.r.t. linear momentum.

But doing the angular part of the collision is tough. For example, a grazing collision could convert a lot of linear momentum to angular, or the other way around. If the two cubes were originally spinning very quickly then they could transfer a lot of this to linear momentum if they caught just right.

Maybe as a start you could model spheres? That will get you some experience.

I read about angular and linear momentum, but I think that it could be simpler. I think that with spheres it would be easier too, but I am working in a project that needs of this collision between two cubes.

I am using a physics library that does this job very well, and it already calculates velocities, positions, inertias of the things. It works around the time a cycle takes to complete, so its movements are all relatives.
But in some moments the collision calculate a wrong result, doing the cubes collide with an object and then it get a large angular velocity.
I think that a energy of the system (always between two rigid bodies) could not be greater than this initial value. This energy could be calculated only with the equation that I mentioned above, right? Or I will really need to work with linear and angular momentum?

I have to rectify about what I have said, the speed will be w*d where d is the distance of any point to the axis of rotation, not to the center of the cube.

Sorry for that.

Thanks USeptim, I will try it.