Collisions in Multiple Dimensions: Introduction

Collisions in day-to-day life do not always occur in one dimension. Additionally, objects may rotate or spin before and after a collision. These objects are often idealized as point masses so that factors like structure, spatial extension, and shape can be excluded for simplicity of calculations.

Conservation of momentum is true in each direction independently. That is, in a two-dimensional collision, momentum is conserved in the x and the y directions independently.

In the two-dimensional collision of two curling stones, the x component of the final momentum is obtained by adding the x components of the initial momenta of the constituent particles, which is also equal to the sum of the x components of the final momenta of the constituent particles.

Similarly, the y component of the final momentum is obtained.

The magnitude of the final momentum vector is obtained using the Pythagorean theorem.