| Exam Board | Edexcel |
|---|---|
| Module | M5 (Mechanics 5) |
| Year | 2013 |
| Session | June |
| Marks | 15 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments of inertia |
| Type | Force at pivot/axis |
| Difficulty | Challenging +1.2 This is a standard compound pendulum problem requiring energy conservation and circular motion analysis. Part (a) is straightforward application of energy methods with the moment of inertia given. Part (b) requires resolving forces at a specific position, which is routine for M5 students. The setup is clear, methods are well-established, and no novel insight is needed—moderately above average due to the multi-step nature and M5 content. |
| Spec | 3.03d Newton's second law: 2D vectors6.02i Conservation of energy: mechanical energy principle |
A uniform circular disc, of radius $r$ and mass $m$, is free to rotate in a vertical plane about a fixed smooth horizontal axis $L$ which is perpendicular to the plane of the disc and passes through a point which is $\frac{1}{4}r$ from the centre of the disc. The disc is held at rest with its centre vertically above the axis. The disc is then slightly disturbed from its rest position.
You may assume without proof that the moment of inertia of the disc about $L$ is $\frac{9mr^2}{16}$.
**(a)** Show that the angular speed of the disc when it has turned through $\frac{\pi}{2}$ is $\sqrt{\frac{8g}{9r}}$.
(4 marks)
**(b)** Find the magnitude of the force exerted on the disc by the axis when the disc has turned through $\frac{\pi}{2}$.
(11 marks)6. A uniform circular disc, of radius $r$ and mass $m$, is free to rotate in a vertical plane about a fixed smooth horizontal axis $L$ which is perpendicular to the plane of the disc and passes through a point which is $\frac { 1 } { 4 } r$ from the centre of the disc. The disc is held at rest with its centre vertically above the axis. The disc is then slightly disturbed from its rest position. You may assume without proof that the moment of inertia of the disc about $L$ is $\frac { 9 m r ^ { 2 } } { 16 }$.
\begin{enumerate}[label=(\alph*)]
\item Show that the angular speed of the disc when it has turned through $\frac { \pi } { 2 }$ is $\sqrt { } \left( \frac { 8 g } { 9 r } \right)$.
\item Find the magnitude of the force exerted on the disc by the axis when the disc has turned through $\frac { \pi } { 2 }$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M5 2013 Q6 [15]}}