# 2D Elastic Collision equations

Does anyone know the equations for 2D elastic collisions.

Galileo
Homework Helper
Don't just learn the equations. Learn the principles behind those equations. You will always have conservation of momentum in any collision. For elastic collisions energy is also conserved. This will give you enough info the solve any collision problem, in principle anyway.

jtbell
Mentor
Conservation of momentum:

$$m_1 v_1 \cos \theta_1 + m_2 v_2 \cos \theta_2 = m_1 v_1^\prime \cos \theta_1^\prime + m_2 v_2^\prime \cos \theta_2^\prime$$

$$m_1 v_1 \sin \theta_1 + m_2 v_2 \sin \theta_2 = m_1 v_1^\prime \sin \theta_1^\prime + m_2 v_2^\prime \sin \theta_2^\prime$$

Conservation of energy:

$$\frac{1}{2} m_1 v_1^2 + \frac{1}{2} m_2 v_2^2 = \frac{1}{2} m_1 {v_1^\prime}^2 + \frac{1}{2} m_2 {v_2^\prime}^2 + Q$$

where $Q$ is the amount of kinetic energy lost in the collision (to "heat" or whatever). For an elastic collision, $Q = 0$.

Thanks for the reply galileo and jtbell. I have done a little reading on conservation of momentum and energy. I also search the internet for the equations and the theories involved in collisions. However i could only find 1D equations.

I would appreciate it if you could point me to any information that could help me to better understand it. I would also like any information on 3D collisions as well. The reason i'm trying to get this information is to write a computer program that simulates collisions.

Galileo