We propose a novel neural network approach, LARP (Learned Articulated Rigid body Physics), to model the dynamics of articulated human motion with contact. Our goal is to develop a faster and more convenient methodological alternative to traditional physics simulators for use in computer vision tasks such as human motion reconstruction from video. To that end we introduce a training procedure and model components that support the construction of a recurrent neural architecture to accurately simulate articulated rigid body dynamics. Our neural architecture supports features typically found in traditional physics simulators, such as modeling of joint motors, variable dimensions of body parts, contact between body parts and objects, and is an order of magnitude faster than traditional systems when multiple simulations are run in parallel. To demonstrate the value of LARP we use it as a drop-in replacement for a state of the art classical non-differentiable simulator in an existing video-based reconstruction framework and show comparative or better 3D human pose reconstruction accuracy.