Challenging +1.2 This is a standard moments of inertia problem requiring application of parallel axis theorem and perpendicular axis theorem to multiple components. While it involves Further Maths content (making it inherently harder), the solution follows a systematic procedure: calculate moment of inertia for each rod about AD using standard formulas and parallel axis theorem, then handle the disc (which rotates about a diameter). The multi-component nature and algebraic manipulation elevate it above average difficulty, but it's a textbook-style exercise without requiring novel geometric insight.
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Three identical uniform rods, \(A B , B C\) and \(C D\), each of mass \(M\) and length \(2 a\), are rigidly joined to form three sides of a square. A uniform circular disc, of mass \(\frac { 2 } { 3 } M\) and radius \(a\), has the opposite ends of one of its diameters attached to \(A\) and \(D\) respectively. The disc and the rods all lie in the same plane (see diagram). Find the moment of inertia of the system about the axis \(A D\).
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\includegraphics[max width=\textwidth, alt={}, center]{c1aae41e-530c-4db4-8959-8afe223c4dbc-2_547_423_260_861}
Three identical uniform rods, $A B , B C$ and $C D$, each of mass $M$ and length $2 a$, are rigidly joined to form three sides of a square. A uniform circular disc, of mass $\frac { 2 } { 3 } M$ and radius $a$, has the opposite ends of one of its diameters attached to $A$ and $D$ respectively. The disc and the rods all lie in the same plane (see diagram). Find the moment of inertia of the system about the axis $A D$.
\hfill \mbox{\textit{CAIE FP2 2013 Q1}}