Challenging +1.2 This is a multi-step Further Maths mechanics problem requiring the parallel axis theorem applied to three separate wire segments, with careful geometric calculation of distances. While systematic, it demands more setup and coordination than a typical A-level question, placing it moderately above average difficulty.
1
A uniform wire, of length \(24 a\) and mass \(m\), is bent into the form of a triangle \(A B C\) with angle \(A B C = 90 ^ { \circ }\), \(A B = 6 a\) and \(B C = 8 a\) (see diagram). Find the moment of inertia of the wire about an axis through \(A\) perpendicular to the plane of the wire.
1
A uniform wire, of length $24 a$ and mass $m$, is bent into the form of a triangle $A B C$ with angle $A B C = 90 ^ { \circ }$, $A B = 6 a$ and $B C = 8 a$ (see diagram). Find the moment of inertia of the wire about an axis through $A$ perpendicular to the plane of the wire.
\hfill \mbox{\textit{CAIE FP2 2008 Q1 [5]}}