Standard +0.8 This is a standard M5/Further Mechanics proof requiring setup of a double integral (or polar coordinates), correct density expression, and careful integration. While the result is well-known, the execution requires solid calculus technique and physical understanding of moment of inertia definition, placing it moderately above average difficulty.
2. A uniform circular disc has radius \(a\) and mass \(m\). Prove, using integration, that the moment of inertia of the disc about an axis through its centre and perpendicular to the plane of the disc is \(\frac { 1 } { 2 } m a ^ { 2 }\).
(Total 5 marks)
2. A uniform circular disc has radius $a$ and mass $m$. Prove, using integration, that the moment of inertia of the disc about an axis through its centre and perpendicular to the plane of the disc is $\frac { 1 } { 2 } m a ^ { 2 }$.\\
(Total 5 marks)\\
\hfill \mbox{\textit{Edexcel M5 2006 Q2 [5]}}