Dynamics of a Spool-Block Atwood System

For many years, Atwood's machine has been used to demonstrate, illustrate, or verify Newton's laws in introductory physics courses. It consists of two objects of different mass that are fastened to the ends of a string that hangs over a pulley. In an idealized situation, one assumes that pulley friction, the string's mass, and changes in the string's length are negligible. Cases in which the pulley's mass is non-negligible may be considered. Advanced students can investigate non-ideal cases in which the string's mass or friction is not negligible or cases in which the masses swing. Computer-based data acquisition tools allow quick and accurate measurements of the acceleration of the objects in the Atwood machine. They enable an instructor to ask probing questions regarding this apparatus while quickly verifying its prevailing physical principles through simple measurements. Two interesting questions that one can ask are: "What is the acceleration of the objects in an Atwood machine when both objects are of equal mass with one being an unraveling spool?" "Is it possible to determine a mass ratio in which the acceleration of the spool is non-zero while the acceleration of the other object is zero?"