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I'm developping a program, I wish if somebody helps me since I'm not good in physics, we know that:

v'1=v1-(j / m1)*n

v'1=v2+(j / m2)*n

1) when we use negative and positive sign? if we change them, there is error sometimes.

2)In 2d, do I have to calculate vx, and vy separately, what about n normal vector? should I do the same or use the magnitude?

And here we talk about relative velocity of j=-(1+e)*rV/1/m1+1/m2,calculate just magnitude or vx and vy, but doe'snt gonna work in rotation:

w'=w+j/i*r*n;

j=j=-(1+e)*rV/(1/m1+1/m2)*n^2*r^2/I*n^2*r^2/I;there will be no wx and wy for vx and vy, I guess magnitude here?

3) Can somebody demonstrate to me how the heck do we passed from:

Vf = Vi+ 2m(vi-Vi)/(m+M);to:

vf=vi-(j / m1)*n;also for rotation;

4) how to add friction:(it's should be negative to the velocity, and f'=uf, with ucoeficient of friction), a dot product with perpendicular to n normalised + j ?

I'm lost here please help; I will appreciate :)