Calculating new velocities of 2 (or, if known, 3)-dimensional spheres (NOT infinitesimally small) after ellastic collision?

Question

I'm trying to calculate the final velocities of two 2D spheres with radius r1 & r2 colliding at some point on the perimeter (or surface area for 3D) of each sphere. How does one do this, taking into account the fact that the spheres don't always collide head on at their center of mass?
(I know this question has been answered many times for infinitesimally small point particles).
Would this just work? Or does this assume that the balls are infinitesimally small?

mr paul · Accepted Answer

Your link for the 3D case will work fine for a 2D case. The concept is the same, you just don’t have z components. Be careful though - note that all the equations in your link only address velocity, and mass is only noted in a caption on a diagram as a weighting factor (nice pun by the author).
You are calculating the velocities, in which case, as Pim notes, the standard momentum and energy equations are fine. If you want to also determine positions, you’ll need to worry about the radii (radiuses) and where the centers of mass are in each circle.

Pim Laeven · Answer

You still have conservation of linear momentum and kinetic energy, and if you know the angle at which they got you can still solve the problem.
$m_1vec{v_1}+m_2vec{v_2} = m_1vec{u_1}+m_2vec{u_2}$
And:
$frac{m_1vec{v_1}^2}{2}+frac{m_2vec{v_2}^2}{2} =  frac{m_1vec{u_1}^2}{2}+frac{m_2vec{u_2}^2}{2}$

Calculating new velocities of 2 (or, if known, 3)-dimensional spheres (NOT infinitesimally small) after ellastic collision?

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