| Exam Board | AQA |
|---|---|
| Module | Further AS Paper 2 Mechanics (Further AS Paper 2 Mechanics) |
| Year | 2023 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circular Motion 1 |
| Type | Angular speed conversion and basic circular motion quantities |
| Difficulty | Moderate -0.8 This is a straightforward circular motion question requiring basic recall of standard formulas (ω = 2πn/t, F = mω²r) with simple arithmetic. The impulse part uses direct application of impulse-momentum theorem with vector addition. All steps are routine calculations with no problem-solving insight required, making it easier than average A-level. |
| Spec | 1.10c Magnitude and direction: of vectors6.03g Impulse in 2D: vector form6.05a Angular velocity: definitions6.05b Circular motion: v=r*omega and a=v^2/r |
| Answer | Marks | Guidance |
|---|---|---|
| \(\sqrt{(-5)^2 + (12)^2} = 13\) Ns | B1 | Condone missing or incorrect units |
| Answer | Marks | Guidance |
|---|---|---|
| \(\mathbf{I} = m\mathbf{v} - m\mathbf{u}\), PI by vectors or magnitudes substituted into formula | M1 | Recalls impulse = change in momentum |
| \(\begin{pmatrix}-5\\12\end{pmatrix} = 5\mathbf{v} - 5\begin{pmatrix}6\\2\end{pmatrix}\), PI by sight of \(\begin{pmatrix}5\\4.4\end{pmatrix}\) | A1 | Uses \(\mathbf{I} = m\mathbf{v} - m\mathbf{u}\) and substitutes given vectors and mass correctly |
| Speed \(= 6.7\) m s\(^{-1}\) | A1 | AWRT 6.7, condone missing or incorrect units |
## Question 5(a):
$\sqrt{(-5)^2 + (12)^2} = 13$ Ns | B1 | Condone missing or incorrect units
---
## Question 5(b):
$\mathbf{I} = m\mathbf{v} - m\mathbf{u}$, PI by vectors or magnitudes substituted into formula | M1 | Recalls impulse = change in momentum
$\begin{pmatrix}-5\\12\end{pmatrix} = 5\mathbf{v} - 5\begin{pmatrix}6\\2\end{pmatrix}$, PI by sight of $\begin{pmatrix}5\\4.4\end{pmatrix}$ | A1 | Uses $\mathbf{I} = m\mathbf{v} - m\mathbf{u}$ and substitutes given vectors and mass correctly
Speed $= 6.7$ m s$^{-1}$ | A1 | AWRT 6.7, condone missing or incorrect units
---5 J\\
10 J\\
20 J
4 Reena is skating on an ice rink, which has a horizontal surface.
She follows a circular path of radius 5 metres and centre $O$\\
She completes 10 full revolutions in 1 minute, moving with a constant angular speed of $\omega$ radians per second.
The mass of Reena is 40 kg\\
4
\begin{enumerate}[label=(\alph*)]
\item Find the value of $\omega$\\
4
\item (i) Find the magnitude of the horizontal resultant force acting on Reena.\\
4 (b) (ii) Show the direction of this horizontal resultant force on the diagram below.\\
\includegraphics[max width=\textwidth, alt={}, center]{78120346-4a16-4545-925a-d6fab4b750e9-03_380_442_2017_861}
5 An impulse of $\left[ \begin{array} { r } - 5 \\ 12 \end{array} \right] \mathrm { N } \mathrm { s }$ is applied to a particle of mass 5 kg which is moving with velocity $\left[ \begin{array} { l } 6 \\ 2 \end{array} \right] \mathrm { m } \mathrm { s } ^ { - 1 }$
5 (a) Calculate the magnitude of the impulse.
5 (b) Find the speed of the particle immediately after the impulse is applied.
\end{enumerate}
\hfill \mbox{\textit{AQA Further AS Paper 2 Mechanics 2023 Q5 [4]}}