| Exam Board | Edexcel |
|---|---|
| Module | M5 (Mechanics 5) |
| Year | 2006 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments of inertia |
| Type | Prove MI by integration |
| Difficulty | Standard +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. |
| Spec | 6.04d Integration: for centre of mass of laminas/solids |
\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]}}