Kinematics and dynamics of a rigid body in plane motion

This article shows a way to derivate the kinematic and dynamic equations of a rigid body in plane motion with respect to the instantaneous center of rotation. The relative-acceleration equation is derived from the relative-velocity equation applied to this point. The angular-momentum and work-energy theorems are obtained by differentiating the angular momentum and the kinetic energy respectively relative to this point. This article offers several novel aspects with respect to existing literature. On the one hand, the deduction of the relative-acceleration equation by using the instantaneous center, and the other hand, the demonstration of the equivalence between the angular-momentum equation and the work-energy equation applied both also to this point. The instantaneous center is usually the most convenient point to solve problems of a rigid body in plain motion in the simplest way. (author)