An ant is moving on thin (negligible thickness) circular wire. How many coordinates do you require to completely describe the motion of the ant?

To completely describe the motion of an ant on a thin circular wire, only one coordinate is required. In classical mechanics, the number of independent parameters needed to specify the configuration of a system is known as its degrees of freedom. A free particle in three-dimensional space typically requires three coordinates (x, y, z). However, when a particle is constrained to move along a specific path, such as a circular wire, its motion is restricted. For a circle of fixed radius, the position of the ant at any moment can be uniquely identified by a single angular variable, theta (θ), which represents its displacement along the circumference. This reduction from three dimensions to one occurs because the constraints of the wire's shape remove the other degrees of freedom, making the motion effectively one-dimensional along the curved path.