M5 January 2006 Q2
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 \(\tfrac{1}{2}ma^2\).
| Scheme | Marks |
|---|---|
| \(\delta m = \dfrac{m}{\pi a^2}\cdot 2\pi x\,\delta x\) | M1 A1 |
| \(\delta I = \dfrac{m}{\pi a^2}\cdot 2\pi x^3\,\delta x\) | M1 |
| \(I = \dfrac{2m}{a^2}\displaystyle\int_0^a x^3\,\mathrm{d}x = \tfrac{1}{2}ma^2\) | M1 A1 |
| (5 marks) |