| Exam Board | Edexcel |
|---|---|
| Module | M5 (Mechanics 5) |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Topic | Impulse and momentum (advanced) |
| Type | Rod and particle collision |
| Difficulty | Challenging +1.8 This M5 question requires conservation of angular momentum about an off-center axis (parallel axis theorem), followed by analyzing forces on a rotating system with both gravitational and centripetal components. While the techniques are standard for M5, the combination of impact mechanics, moment of inertia about a tangent, and force analysis at a specific instant requires careful multi-step reasoning and is significantly harder than typical A-level mechanics questions. |
| Spec | 6.02i Conservation of energy: mechanical energy principle6.03f Impulse-momentum: relation6.04b Find centre of mass: using symmetry |
A uniform circular disc has mass $m$, centre $O$ and radius $2a$. It is free to rotate about a fixed smooth horizontal axis $L$ which lies in the same plane as the disc and which is tangential to the disc at the point $A$. The disc is hanging at rest in equilibrium with $O$ vertically below $A$ when it is struck at $O$ by a particle of mass $m$. Immediately before the impact the particle is moving perpendicular to the plane of the disc with speed $3\sqrt{ag}$. The particle adheres to the disc at $O$.
\begin{enumerate}[label=(\alph*)]
\item Find the angular speed of the disc immediately after the impact.
[5]
\end{enumerate}
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find the magnitude of the force exerted on the disc by the axis immediately after the impact.
[6]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M5 Q6 [11]}}