Is it possible to separate the angular and linear momentum and treat them separately in a system such as an inverted pendulum? For example, a pole on a platform balancing on its end. If it is unbalanced so that it falls off the platform, it goes through motion like an inverted pendulum until it leaves the platform at which point it has angular momentum around its COM and linear momentum of its COM with vertical and horizontal components (correct me if I'm wrong here). Is the horizontal component of linear momentum of its COM the same just before it breaks contact with the platform as it is when it is falling? If so, does that mean that angular momentum could be ignored when calculating horizontal linear acceleration? Finally, can anyone point me to the kind of calculations I could do to discover the linear horizontal momentum change generated in this scenario?