| Exam Board | Edexcel |
|---|---|
| Module | M5 (Mechanics 5) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Topic | Circular Motion 2 |
| Type | Collision/impulse during circular motion |
| Difficulty | Challenging +1.8 This is a challenging M5 rotational dynamics problem requiring multiple sophisticated steps: finding angular velocity of particle pre-collision using energy conservation, applying conservation of angular momentum through an inelastic collision, then using energy conservation post-collision with a composite body. Part (b) requires careful setup of the energy equation with two different moment arms and solving a non-trivial trigonometric equation. While the techniques are standard for M5, the multi-stage nature, careful bookkeeping of the composite system, and the specific trigonometric result make this significantly harder than average A-level questions. |
| Spec | 6.02i Conservation of energy: mechanical energy principle6.03i Coefficient of restitution: e6.04d Integration: for centre of mass of laminas/solids |
A uniform rod $PQ$, of mass $m$ and length $3a$, is free to rotate about a fixed smooth horizontal axis $L$, which passes through the end $P$ of the rod and is perpendicular to the rod. The rod hangs at rest in equilibrium with $Q$ vertically below $P$. One end of a light inextensible string of length $2a$ is attached to the rod at $P$ and the other end is attached to a particle of mass $3m$. The particle is held with the string taut, and horizontal and perpendicular to $L$, and is then released. After colliding, the particle sticks to the rod forming a body $B$.
\begin{enumerate}[label=(\alph*)]
\item Show that the moment of inertia of $B$ about $L$ is $15ma^2$.
[2]
\end{enumerate}
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Show that $B$ first comes to instantaneous rest after it has turned through an angle $\arccos\left(\frac{9}{25}\right)$.
[10]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M5 Q3 [12]}}