Description

This simulation illustrates how a central force with magnitude m*v^2/r produces circular motion according to Newton's laws (and Corollary 1 of the Principia). The main view show a particle (magenta) and a force center (orange). During each time step the particle experiences a constant acceleration in direction that is toward the center at the beginning of the time step. The magnitude of the acceleration is v^2/r using the values of v and r at the beginning of the time step. The motion of the particle during the time step will be along the diagonal of a parallelogram formed by the displacement due to the constant acceleration (shown in red) and the displacement due to the particle's inertial motion (shown in blue). The simulation shows each of these displacements in sequence. The (optional) velocity vector at each moment is displayed in green.

The user can play/pause/reset the simulation, change the time step, and change the number of substeps per time step (to slow the simulation and more clearly show the two displacements being executed). As the time step approaches zero (i.e. a continuous centripetal force) the path of the particle approaches a circle centered on the force center.