Two-Dimensional Tetherball Explorer

Live Script exploring a ball wrapping a tether around a pole in two dimensions.

This educational Live Script explores the classical mechanics of a tethered ball orbiting a pole as its tether wraps around it. This model approximates motion in the game of tetherball in the absence of gravity. A calculation based on Newton's 2nd law leads to two coupled 2nd-order differential equations, which are solved numerically. It is shown that energy conservation can be used to reduce the problem to a single first-order differential equation when the constraint is built in. The numerical results for the two methods and an exact analytic solution to the first-order differential equation are compared.

This script may interest students and instructors of physics. It illustrates introductory mechanics and numerical solution of ordinary differential equations. Additional educational Live Scripts by the author may be found here.