| Exam Board | Edexcel |
|---|---|
| Module | M5 (Mechanics 5) |
| Session | Specimen |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Impulse and momentum (advanced) |
| Type | Rod and particle collision |
| Difficulty | Challenging +1.8 This M5 question requires conservation of angular momentum for an oblique collision, calculating moment of inertia using parallel axis theorem (disc rotating about circumference point), then energy conservation for rotational motion. Multiple advanced mechanics concepts must be correctly applied in sequence, with non-trivial geometry (horizontal diameter strike point). Significantly harder than typical A-level questions but standard for M5 module. |
| Spec | 6.03f Impulse-momentum: relation6.03g Impulse in 2D: vector form6.04d Integration: for centre of mass of laminas/solids6.05f Vertical circle: motion including free fall |
| Answer | Marks | Guidance |
|---|---|---|
| \(I = \left(\frac{1}{2} \times 2ma^2 + 2ma^2\right) + m\left(a\sqrt{2}\right)^2 = 5ma^2\) | M1 A1 A1 A1 | |
| \(ma\sqrt{20ag} = 5ma^2\omega\) | M1 A1 | |
| \(\omega = \sqrt{\frac{4g}{5a}}\) | A1 | (7 marks) |
| Answer | Marks | Guidance |
|---|---|---|
| PE Gain \(= 2mga\) | A1 | |
| KE Loss \(= \frac{1}{2} \times 5ma^2 \times \frac{4g}{5a} = 2mga\) | M1 A1 | (3 marks) |
Total: 10 marks
## Part (a)
$I = \left(\frac{1}{2} \times 2ma^2 + 2ma^2\right) + m\left(a\sqrt{2}\right)^2 = 5ma^2$ | M1 A1 A1 A1 |
$ma\sqrt{20ag} = 5ma^2\omega$ | M1 A1 |
$\omega = \sqrt{\frac{4g}{5a}}$ | A1 | (7 marks)
## Part (b)
PE Gain $= 2mga$ | A1 |
KE Loss $= \frac{1}{2} \times 5ma^2 \times \frac{4g}{5a} = 2mga$ | M1 A1 | (3 marks)
Total: 10 marks
---A uniform circular disc, of mass $2m$ and radius $a$, is free to rotate in a vertical plane about a fixed, smooth horizontal axis through a point of its circumference. The axis is perpendicular to the plane of the disc. The disc hangs in equilibrium. A particle $P$ of mass $m$ is moving horizontally in the same plane as the disc with speed $\sqrt{20ag}$. The particle strikes, and adheres to, the disc at one end of its horizontal diameter.
\begin{enumerate}[label=(\alph*)]
\item Find the angular speed of the disc immediately after $P$ strikes it. [7]
\item Verify that the disc will turn through an angle of $90°$ before first coming to instantaneous rest. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M5 Q4 [10]}}