Summarizing Collisions of Point Masses in Two Dimensions

Summary

• The approach to two-dimensional collisions is to choose a convenient coordinate system and break the motion into components along perpendicular axes. Choose a coordinate system with the \(x\)-axis parallel to the velocity of the incoming particle.
• Two-dimensional collisions of point masses where mass 2 is initially at rest conserve momentum along the initial direction of mass 1 (the \(x\)-axis), stated by \({m}_{1}{v}_{1}={m}_{1}{v\prime }_{1}\phantom{\rule{0.25em}{0ex}}\text{cos}\phantom{\rule{0.25em}{0ex}}{\theta }_{1}+{m}_{2}{v\prime }_{2}\phantom{\rule{0.25em}{0ex}}\text{cos}\phantom{\rule{0.25em}{0ex}}{\theta }_{2}\) and along the direction perpendicular to the initial direction (the \(y\)-axis) stated by \(0={m}_{1}{v\prime }_{1y}+{m}_{2}{v\prime }_{2y}\).
• The internal kinetic before and after the collision of two objects that have equal masses is
  \(\frac{1}{2}{{\text{mv}}_{1}}^{2}=\frac{1}{2}{{\text{mv}\prime }_{1}}^{2}+\frac{1}{2}{{\text{mv}\prime }_{2}}^{2}+{\text{mv}\prime }_{1}{v\prime }_{2}\phantom{\rule{0.25em}{0ex}}\text{cos}\left({\theta }_{1}-{\theta }_{2}\right).\)
• Point masses are structureless particles that cannot spin.

Glossary

point masses

structureless particles with no rotation or spin