Direct and Oblique Impact
The animation in the last slide shows 2 particles which impact in an oblique manner. Here spherical particles of mass m1 and m2 have initial velocities v1 and v2 in the same plane and approach each other on a collision course. The directions of the velocity vectors are measured from the direction tangent to the contacting surfaces. Thus, the initial velocity components along the t and n-axes are 
. Note that (v1)n is a negative quantity for the particular coordinate system and initial velocities shown. Shades of 3 different situations are shown below.
For given initial conditions of m1, m2, (v1)n, ( v1)t and (v2)n, (v2)t , there will be four unknowns, namely (v1')n, (v1')t, (v2')n and (v2')t . The four needed equations are obtained as follows:
(1) Momentum of the system in the n-direction. This gives,
(2) and (3) The momentum for each particle is conserved in the t-direction since there is no impulse on either particle in the t-direction.Thus
