Analogies between Kinematics of Linear and Angular Motion

The dynamical variables describing one-dimensional linear and angular (including circular) motion show systematic analogous relationships with one another. For angular motion, the inertial variable analogous to mass for linear motion is the moment of inertia, given by , where is the instantaneous radius of curvature. The configuration variable for linear motion is , while that of angular motion is . From these the other dynamical variables for velocity, acceleration, momentum and energy can be built. We also show the forms of Newton's second law and the Lagrangian and Hamiltonian functions, and , respectively. The potential energy is represented by the function or . The force and torque for conservative systems are given by and .