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diff --git a/Master/texmf-dist/doc/latex/exam-n/sample/dynamical2.tex b/Master/texmf-dist/doc/latex/exam-n/sample/dynamical2.tex new file mode 100644 index 00000000000..517ae849205 --- /dev/null +++ b/Master/texmf-dist/doc/latex/exam-n/sample/dynamical2.tex @@ -0,0 +1,24 @@ +\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} |