A Zenonian supertask involving an infinite number of identical colliding balls is generalized to include balls with different masses. Under the restriction that the total mass of all the balls is finite, classical mechanics leads to velocities that have no upper limit. Relativistic mechanics results in velocities bounded by that of light, but energy and momentum are not conserved, implying indeterminism. The notion that both determinism and the conservation laws might be salvaged via photon creation is shown to be flawed.

There is broad consensus as to what a rigid body is in classical mechanics. The idea is that a rigid body is an undeformable body. In this paper I show that, if this identification is accepted, there are therefore rigid bodies which are unstable. Instability here means that the evolution of certain rigid bodies, even when isolated from all external influence, may be such that their identity is not preserved over time. The result is followed by analyzing supertasks that are (...) possible in infinite systems of rigid bodies. I propose that, if we wish to preserve our original intuitions regarding the necessary stability of rigid bodies, then the concept of rigid body must be clearly distinguished from that of undeformable body. I therefore put forward a new definition of rigid body. Only the concept of undeformable body is holistic and every connected part of a rigid body in this new sense is always a rigid body in this new sense. Finally, I briefly discuss the connection between this conceptual distinction and the dimensionality of space, thereby enabling it to be supported from a new and interesting perspective. (shrink)

In this paper, an example is presented for a dynamic system analysable in the framework of the mechanics of rigid bodies. Interest in the model lies in three fundamental features. First, it leads to a paradox in classical mechanics which does not seem to be explainable with the conceptual resources currently available. Second, it is possible to find a solution to it by extending in a natural way the idea of global interaction in the context of what is called interaction (...) by impenetrability. Third, the solution presented throws light on a problem posed and discussed in the recent literature in connection with the mass conservation principle. (shrink)