# Calculating a 2D collision between two perfectly circular disks [duplicate]

Assume I have two disks, $p_1$ and $p_2$, of radius $r$, with their own velocities (preferably in $(x,y)$ form, but $(m, \theta)$ works too) and masses (unit-less, but same unit) collide in two dimensions, how can I compute their resulting velocities?

I was looking around on the internet and it seems like every calculation assumes that one of them is at rest, but both of mine will be moving.

Wikipedia has this bit, but it assumes that I know how to calculate the angle of deflection of the system, $\theta$, but that's even more confusing.

I'm pretty lost. What do I do?

• You can perform a Galilei transformation, such that one of the particles is at rest. Then, the problem just reduces to one that you knew already. If you don't want this, you could use conservation of moment and energy. – Bernhard Feb 26 '13 at 17:46
• Do the particles have the same radii? Also, since you said you've found calculations with one body at rest: why don't you try doing your calculation by transforming to the rest frame of one particle, using the sources you've found to calculate the result, then transform back to your original frame? – jeffdk Feb 26 '13 at 17:48
• Possible duplicate: physics.stackexchange.com/q/53877/2451 – Qmechanic Feb 26 '13 at 17:52
• @Bernhard I am not sure what a Galilei transformation is. – tekknolagi Feb 26 '13 at 21:32
• @jeffdk they do not have the same radii. – tekknolagi Feb 26 '13 at 21:33

At the time of collision join the centres of the to disk by a line now resolve the momentum of each disk in parallel and perpendicular to the line and apply the conservation of momentum. And in this case sin(theta)= d/(r+R) where d is the distance between parallel line drawn from the center of two discs. Value of d or theta would be given in the question if not wait for some time i will find and post the way to find theta without d. 