Edexcel M5 2006 June — Question 1 6 marks

Exam BoardEdexcel
ModuleM5 (Mechanics 5)
Year2006
SessionJune
Marks6
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicMoments of inertia
TypeProve MI by integration
DifficultyStandard +0.3 This is a standard M5 moment of inertia question requiring straightforward integration for part (a) and a routine application of parallel strips or rods for part (b). While it involves calculus and 3D visualization, the techniques are textbook exercises with no novel problem-solving required, making it slightly easier than average for A-level mechanics.
Spec6.04d Integration: for centre of mass of laminas/solids

  1. Prove, using integration, that the moment of inertia of a uniform rod, of mass \(m\) and length \(2a\), about an axis perpendicular to the rod through one end is \(\frac{4}{3}ma^2\). [3]
  2. Hence, or otherwise, find the moment of inertia of a uniform square lamina, of mass \(M\) and side \(2a\), about an axis through one corner and perpendicular to the plane of the lamina. [3]

\begin{enumerate}[label=(\alph*)]
\item Prove, using integration, that the moment of inertia of a uniform rod, of mass $m$ and length $2a$, about an axis perpendicular to the rod through one end is $\frac{4}{3}ma^2$. [3]

\item Hence, or otherwise, find the moment of inertia of a uniform square lamina, of mass $M$ and side $2a$, about an axis through one corner and perpendicular to the plane of the lamina. [3]
\end{enumerate}

\hfill \mbox{\textit{Edexcel M5 2006 Q1 [6]}}