| Exam Board | WJEC |
|---|---|
| Module | Further Unit 3 (Further Unit 3) |
| Year | 2022 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circular Motion 1 |
| Type | Conical pendulum – particle on horizontal surface |
| Difficulty | Moderate -0.8 This is a straightforward circular motion question requiring only direct application of standard formulas: ω = v/r and T = mv²/r (or T = mrω²). Both parts involve single-step calculations with no conceptual challenges or problem-solving required, making it easier than average even for Further Maths students. |
| Spec | 6.05a Angular velocity: definitions |
| Answer | Marks | Guidance |
|---|---|---|
| \(\omega = 4\) (rad s\(^{-1}\)) | M1, A1[2] | Used; cao |
| Answer | Marks | Guidance |
|---|---|---|
| \(T = 38 \cdot 4\) (N) or \(\frac{192}{5}\) | M1, A1[2] | Used with \(a = \frac{v^2}{r}\) or \(\omega^2 r\); FT their \(\omega\) from (a) |
## Part (a)
Angular velocity $\omega = \frac{v}{r}$
$\omega = \frac{8}{2}$
$\omega = 4$ (rad s$^{-1}$) | M1, A1[2] | Used; cao
## Part (b)
N2L towards centre $O$
Tension in the string $T = 1 \cdot 2a$ where $a = \frac{v^2}{r} = \frac{\omega^2 r}{1}$
$T = 1 \cdot 2 \times \frac{8^2}{2}$ or $T = 1 \cdot 2 \times 4^2 \times 2$
$T = 38 \cdot 4$ (N) or $\frac{192}{5}$ | M1, A1[2] | Used with $a = \frac{v^2}{r}$ or $\omega^2 r$; FT their $\omega$ from (a)
**Total for Question 1: 4**
---A particle of mass 1.2 kg is attached to one end of a light inextensible string of length 2 m. The other end of the string is fixed to a point O on a smooth horizontal surface. With the string taut, the particle moves on the surface with constant speed $8\text{ ms}^{-1}$ in a horizontal circle with centre O.
\begin{enumerate}[label=(\alph*)]
\item Find the angular velocity of the particle about O. [2]
\item Calculate the tension in the string. [2]
\end{enumerate}
\hfill \mbox{\textit{WJEC Further Unit 3 2022 Q1 [4]}}