A rigid body physics engine can help us accurately model physical behaviour between entities in computer simulations. In this project we design and implement a 2D rigid body physics engine capable of performing at real-time speeds. This paper discusses the steps involved in building such an engine. We begin by discussing the basic techniques used in physical simulation including time stepping and unconstrained motion of oriented bodies using numerical integration. We present methods for detecting collisions between a variety of types of bodies as well as solutions for obtaining the proper data necessary to resolve these collisions. An iterative impulse-based method for solving collisions and modelling friction is presented.