= 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 is
$$
\boxed{\frac{d\mathbf J}{dt}=\boldsymbol\tau_{\rm ext}=0.}
$$
Internal 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.
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