= Solution
About a chosen origin $O$, a particle has <angular momentum> $\mathbf L=\mathbf r\times\mathbf p$. A body has $\mathbf L=\sum_i\mathbf r_i\times\mathbf p_i$, or the corresponding integral for a continuous <mass> distribution. For a fixed origin in an <inertial frame>,
$$
\boxed{\frac{d\mathbf L}{dt}=\boldsymbol\tau_{\rm external};\qquad\boldsymbol\tau_{\rm external}=0\ \Longrightarrow\ \mathbf L=\text{constant}.}
$$
Internal central pair <forces> cancel in the total <torque>. About a fixed origin, a <central force> conserves a particle's <angular momentum>; zero net <force> alone is insufficient if an external couple remains.
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