OCR M4 2003 June — Question 2 5 marks

Exam BoardOCR
ModuleM4 (Mechanics 4)
Year2003
SessionJune
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicMoments of inertia
TypeComposite body MI calculation
DifficultyStandard +0.8 This is a composite body MOI problem requiring decomposition of an irregular lamina into rectangles, application of parallel axis theorem, and perpendicular axis theorem. While the techniques are standard for M4, the multi-step calculation with careful bookkeeping of multiple components and two parts makes it moderately challenging, above average difficulty.
Spec6.04d Integration: for centre of mass of laminas/solids

2 \includegraphics[max width=\textwidth, alt={}, center]{de53978b-aa96-4fa2-a928-81a16450154e-2_462_490_610_834} The diagram shows a uniform lamina \(A B C D E F\) in which all the corners are right angles. The mass of the lamina is \(3 m\).
  1. Show that the moment of inertia of the lamina about \(A B\) is \(3 m a ^ { 2 }\).
  2. Find the moment of inertia of the lamina about an axis perpendicular to the lamina and passing through \(A\).

2\\
\includegraphics[max width=\textwidth, alt={}, center]{de53978b-aa96-4fa2-a928-81a16450154e-2_462_490_610_834}

The diagram shows a uniform lamina $A B C D E F$ in which all the corners are right angles. The mass of the lamina is $3 m$.\\
(i) Show that the moment of inertia of the lamina about $A B$ is $3 m a ^ { 2 }$.\\
(ii) Find the moment of inertia of the lamina about an axis perpendicular to the lamina and passing through $A$.

\hfill \mbox{\textit{OCR M4 2003 Q2 [5]}}