| Exam Board | Edexcel |
|---|---|
| Module | M5 (Mechanics 5) |
| Year | 2014 |
| Session | June |
| Marks | 15 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Simple Harmonic Motion |
| Type | Small oscillations: rigid body compound pendulum |
| Difficulty | Challenging +1.2 This is a standard M5 rigid body dynamics problem requiring parallel axis theorem, energy conservation, and torque equations. Parts (a)-(c) are routine applications of standard techniques, but part (d) requires recognizing that when the reaction is perpendicular to the rod, the radial component of weight must provide the centripetal force—a moderately challenging insight that elevates this above typical textbook exercises. |
| Spec | 6.04d Integration: for centre of mass of laminas/solids6.05e Radial/tangential acceleration6.05f Vertical circle: motion including free fall |
A uniform rod $AB$, of mass $m$ and length $2a$, is free to rotate in a vertical plane about a fixed smooth horizontal axis $L$. The axis $L$ is perpendicular to the rod and passes through the point $P$ of the rod, where $AP = \frac{2}{3}a$.
\begin{enumerate}[label=(\alph*)]
\item Find the moment of inertia of the rod about $L$.
[3]
\end{enumerate}
The rod is held at rest with $B$ vertically above $P$ and is slightly displaced.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find the angular speed of the rod when $PB$ makes an angle $\theta$ with the upward vertical.
[4]
\item Find the magnitude of the angular acceleration of the rod when $PB$ makes an angle $\theta$ with the upward vertical.
[3]
\item Find, in terms of $g$ and $a$ only, the angular speed of the rod when the force acting on the rod at $P$ is perpendicular to the rod.
[5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M5 2014 Q5 [15]}}