Comparative kinetics of the snowball respect to other dynamical objects

Abstract

We examine the kinetics of a snowball that is gaining mass while is rolling downhill. This dynamical system combines rotational motion with effects involving the variation of mass. In order to understand the consequences of both effects we compare its behavior with the one of some objects in which they are absent, so we compare the snowball with a ball with no mass variation and with a skier with no mass variation nor rotational motion. Environmental conditions are also included. We conclude that the comparative velocity of the snowball respect to the other objects is particularly sensitive to the hill profile and also depend on some retardation factors such as the friction, the drag force, the rotation, and the increment of mass (inertia). We emphasize that the increase of inertia could surprisingly diminish the retardation effect owing to the drag force. Additionally, when an exponential trajectory is assumed, the maximum velocity for the snowball can be reached at an intermediate step of the trip.