\documentclass[final]{exam-n}
\begin{document}
\begin{question}{30} \comment{by John Brown}
Give the equations of motion for $i=1,\ldots, N$ particles of
masses $m_i$ and positions $r_i(t)$ under the action of mutual
gravity alone in an arbitrary inertial frame.
\partmarks{4}
Use these to derive the following conservation laws of the system:
\part Constancy of linear momentum -- i.e., centre of mass fixed in a
suitable inertial frame. \partmarks{4}
\part Constancy of angular momentum. \partmarks{6}
\part Constancy of total energy. \partmarks{8}
How many integrals of motion exist in total?
\partmarks{2}
Derive the moment of inertia of the system and demonstrate its
relevance to criteria for escape of particles from the system.
\partmarks{6}
\end{question}
\end{document}