= Solution
About a fixed origin in an <inertial frame>, the <angular momentum> and <torque> are
$$
\boxed{\mathbf L=\mathbf r\times m\mathbf v,\qquad
\boldsymbol\tau=\mathbf r\times\mathbf F.}
$$
For a specified fixed axis with unit vector $\widehat{\mathbf n}$, use the projections $L_n=\widehat{\mathbf n}\cdot\mathbf L$ and $\tau_n=\widehat{\mathbf n}\cdot\boldsymbol\tau$. The <mass> is constant. Differentiating and applying <Newton's second law>,
$$
\frac{d\mathbf L}{dt}
=\mathbf v\times m\mathbf v+\mathbf r\times m\dot{\mathbf v}
=0+\mathbf r\times\mathbf F
=\boxed{\boldsymbol\tau}.
$$
Hence $\dot L_n=\tau_n$ for the fixed axis. If the net <torque> vanishes, the corresponding <angular momentum> is conserved. Fixing the origin and axis is essential to this unmodified form of the law.
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