= Solution
For a <central potential> use $L=m|\dot{\mathbf r}|^2/2-V(|\mathbf r|)$. An infinitesimal <rotation> about any constant unit <vector> $\mathbf n$ has $\phi=0$ and $\boldsymbol\psi=\mathbf n\times\mathbf r$. <Noether's theorem> gives $Q=m\dot{\mathbf r}\cdot(\mathbf n\times\mathbf r)=\mathbf n\cdot\mathbf L$, where $\mathbf L=\mathbf r\times m\dot{\mathbf r}$. Since $\mathbf n$ is arbitrary, every component of <angular momentum> is conserved. A <time-translation symmetry> has $\phi=1$, $\boldsymbol\psi=0$, giving $Q=-E$ and
$$
\boxed{\mathbf L=\mathbf r\times m\dot{\mathbf r},\qquad E=\frac12m|\dot{\mathbf r}|^2+V(r)}
$$
as conserved quantities.
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