| Exam Board | AQA |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2010 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circular Motion 1 |
| Type | Conical pendulum – horizontal circle in free space (no surface) |
| Difficulty | Moderate -0.3 This is a standard conical pendulum problem requiring basic trigonometry (radius = L sin θ) and resolving forces with circular motion (T cos θ = mg, T sin θ = mrω²). The setup is straightforward with clear given values, making it slightly easier than average but still requiring proper application of mechanics principles. |
| Spec | 6.05b Circular motion: v=r*omega and a=v^2/r6.05c Horizontal circles: conical pendulum, banked tracks |
| Answer | Marks | Guidance |
|---|---|---|
| \(r = 1.2\sin\theta\) | B1 | \(1.2\cos\theta\) scores 0 marks |
| Answer | Marks | Guidance |
|---|---|---|
| Resolve horizontally: \(T\sin\theta = m\omega^2 r\) | M1A1 | \(T\cos\theta = m\omega^2 r\) etc scores M1 (+ second M1) |
| \(T\sin\theta = 4 \times 5^2 \times 1.2\sin\theta\), so \(T = 120\) | A1 | |
| Resolve vertically: \(T\cos\theta = 4g\) | M1A1 | M1 for \(\tan\theta = \frac{30\sin\theta}{g}\) |
| \(\cos\theta = 0.32666\) | ||
| \(\theta = 70.9°\) or \(1.24^c\) | A1 | Total: 6 |
## Question 6:
**Part (a):**
| $r = 1.2\sin\theta$ | B1 | $1.2\cos\theta$ scores 0 marks |
**Part (b):**
| Resolve horizontally: $T\sin\theta = m\omega^2 r$ | M1A1 | $T\cos\theta = m\omega^2 r$ etc scores M1 (+ second M1) |
| $T\sin\theta = 4 \times 5^2 \times 1.2\sin\theta$, so $T = 120$ | A1 | |
| Resolve vertically: $T\cos\theta = 4g$ | M1A1 | M1 for $\tan\theta = \frac{30\sin\theta}{g}$ |
| $\cos\theta = 0.32666$ | | |
| $\theta = 70.9°$ or $1.24^c$ | A1 | Total: 6 |
---6 A particle, of mass 4 kg , is attached to one end of a light inextensible string of length 1.2 metres. The other end of the string is attached to a fixed point $O$. The particle moves in a horizontal circle at a constant speed. The angle between the string and the vertical is $\theta$.\\
\includegraphics[max width=\textwidth, alt={}, center]{06b431ca-d3a8-46d6-b9f8-bac08d3fd51e-4_529_554_1580_737}
\begin{enumerate}[label=(\alph*)]
\item Find the radius of the horizontal circle in terms of $\theta$.
\item The angular speed of the particle is 5 radians per second. Find $\theta$.
\end{enumerate}
\hfill \mbox{\textit{AQA M2 2010 Q6 [7]}}