 Solution

Conservation of angular momentum means that the total angular momentum of a system about a chosen fixed origin in an inertial frame stays constant. Its dynamical condition isInternal torques cancel for the complete isolated mechanical system. If only the component of external torque about an axis vanishes, only that angular momentum component is necessarily conserved. The skater's upright spin uses this axial statement: vertical weight and support provide negligible vertical-axis torque, and frictional torque is neglected. The skater need not conserve rotational kinetic energy while changing the internal configuration.