| Exam Board | OCR |
|---|---|
| Module | Further Mechanics AS (Further Mechanics AS) |
| Year | 2021 |
| Session | November |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circular Motion 1 |
| Type | Conical pendulum – particle on horizontal surface |
| Difficulty | Easy -1.2 This is a straightforward application of basic circular motion formulas (ω = 2π/T, v = rω, a = v²/r) with direct substitution of given values. All parts are standard recall with minimal problem-solving, making it easier than average A-level questions which typically require more synthesis or multi-step reasoning. |
| Spec | 6.05a Angular velocity: definitions6.05b Circular motion: v=r*omega and a=v^2/r |
| Answer | Marks | Guidance |
|---|---|---|
| \(\omega = 2\pi / 0.84\) soi | M1 | Correct formula for angular velocity used |
| awrt \(7.48\) rad s\(^{-1}\) | A1 | \(\left(\frac{50}{21}\pi\right)\) |
| Answer | Marks | Guidance |
|---|---|---|
| \(v = 2.8 \times\) "7.48..." or \(2\pi \times 2.8 / 0.84\) | M1 | Correct formula for speed used \(\left(\frac{20}{3}\pi\right)\); FT their value for \(\omega\) if used |
| awrt \(20.9\) m s\(^{-1}\) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| \(a =\) "20.9..."\(^2 / 2.8\) or \(2.8 \times\) "7.48..."\(^2\) or "20.9..." \(\times\) "7.48..." | M1 | Any correct formula for acceleration used; FT their value for \(v\) if used |
| awrt \(157\) (or \(156\)) ms\(^{-2}\) | A1 | \(156\) if rounded values used \(\left(\frac{1000}{63}\pi^2\right)\) |
| Answer | Marks | Guidance |
|---|---|---|
| ...towards \(O\) | B1 | Any indication that the acceleration is towards the centre of the circle |
# Question 1:
## Part (a)
$\omega = 2\pi / 0.84$ soi | **M1** | Correct formula for angular velocity used
awrt $7.48$ rad s$^{-1}$ | **A1** | $\left(\frac{50}{21}\pi\right)$
## Part (b)
$v = 2.8 \times$ "7.48..." or $2\pi \times 2.8 / 0.84$ | **M1** | Correct formula for speed used $\left(\frac{20}{3}\pi\right)$; FT their value for $\omega$ if used
awrt $20.9$ m s$^{-1}$ | **A1** |
## Part (c)
$a =$ "20.9..."$^2 / 2.8$ or $2.8 \times$ "7.48..."$^2$ or "20.9..." $\times$ "7.48..." | **M1** | Any correct formula for acceleration used; FT their value for $v$ if used
awrt $157$ (or $156$) ms$^{-2}$ | **A1** | $156$ if rounded values used $\left(\frac{1000}{63}\pi^2\right)$
## Part (d)
...towards $O$ | **B1** | Any indication that the acceleration is towards the centre of the circle
---1 One end of a light inextensible string of length 2.8 m is attached to a fixed point $O$ on a smooth horizontal table. The other end of the string is attached to a particle $P$ which moves on the table, with the string taut, in a circular path around $O$. The speed of $P$ is constant and $P$ completes each circle in 0.84 seconds.
\begin{enumerate}[label=(\alph*)]
\item Find the magnitude of the angular velocity of $P$.
\item Find the speed of $P$.
\item Find the magnitude of the acceleration of $P$.
\item State the direction of the acceleration of $P$.
\end{enumerate}
\hfill \mbox{\textit{OCR Further Mechanics AS 2021 Q1 [7]}}