| Exam Board | Edexcel |
|---|---|
| Module | M5 (Mechanics 5) |
| Year | 2006 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Simple Harmonic Motion |
| Type | Small oscillations: rigid body compound pendulum |
| Difficulty | Standard +0.8 This is a standard compound pendulum problem requiring moment of inertia calculation (I = 4ma²/3), torque equation setup, small angle approximation (sin θ ≈ θ), and identification of SHM form to find period. While it involves multiple steps and M5-level mechanics, it follows a well-established template that students practice extensively. The 6-mark allocation and straightforward structure place it moderately above average difficulty. |
| Spec | 6.02i Conservation of energy: mechanical energy principle6.03b Conservation of momentum: 1D two particles6.03f Impulse-momentum: relation6.04c Composite bodies: centre of mass6.05e Radial/tangential acceleration |
4. A uniform $\operatorname { rod } A B$, of mass $m$ and length $2 a$, is free to rotate in a vertical plane about a fixed smooth horizontal axis through $A$ and perpendicular to the plane. The rod hangs in equilibrium with $B$ below $A$. The rod is rotated through a small angle and released from rest at time $t = 0$.
\begin{enumerate}[label=(\alph*)]
\item Show that the motion of the rod is approximately simple harmonic.
\item Using this approximation, find the time $t$ when the rod is first vertical after being released.\\
(Total 6 marks)
\end{enumerate}
\hfill \mbox{\textit{Edexcel M5 2006 Q4 [6]}}