Edexcel M5 Specimen — Question 2 7 marks

Exam BoardEdexcel
ModuleM5 (Mechanics 5)
SessionSpecimen
Marks7
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Mark schemeDownload PDF ↗
TopicMoments of inertia
TypeComposite body MI calculation
DifficultyStandard +0.8 This M5 question requires deriving a standard moment of inertia formula via integration (part a), then applying perpendicular axis theorem and parallel axis theorem to a composite body (part b). While the integration is straightforward, correctly decomposing the square into four rods and applying the theorems systematically requires solid understanding of rotational mechanics—above average difficulty but standard for M5.
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 its centre is \(\frac{1}{3}ma^2\). [3]
A uniform wire of mass \(4m\) and length \(8a\) is bent into the shape of a square.
  1. Find the moment of inertia of the square about the axis through the centre of the square perpendicular to its plane. [4]

\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 its centre is $\frac{1}{3}ma^2$. [3]
\end{enumerate}

A uniform wire of mass $4m$ and length $8a$ is bent into the shape of a square.

\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find the moment of inertia of the square about the axis through the centre of the square perpendicular to its plane. [4]
\end{enumerate}

\hfill \mbox{\textit{Edexcel M5  Q2 [7]}}