| Exam Board | Edexcel |
|---|---|
| Module | M3 (Mechanics 3) |
| Year | 2018 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circular Motion 1 |
| Type | Rotating disc with friction |
| Difficulty | Standard +0.3 This is a standard circular motion problem requiring students to equate centripetal force to maximum friction (μR = μmg) and rearrange to get the given inequality. It's slightly easier than average because it's a direct application of F=mrω² with friction providing the centripetal force, requiring only 2-3 steps with no novel insight. |
| Spec | 6.05c Horizontal circles: conical pendulum, banked tracks |
| Answer | Marks | Guidance |
|---|---|---|
| Working/Answer | Marks | Guidance |
| \(F \leqslant \mu mg\) or \(F = \mu mg\) or \(F \leqslant \mu R\) and \(R = mg\) or \(F = \mu R\) and \(R = mg\) | B1 | Award for any of these four statements seen |
| \(F = mr\omega^2\) or \(F \geq mr\omega^2\) | M1A1 | Equation of motion horizontally; acceleration in either form; can be inequality; must include \(F\) |
| \(mr\omega^2 \leqslant \mu mg\) | dM1 | Eliminate \(F\); must now have an inequality |
| \(\omega \leqslant \sqrt{\dfrac{\mu g}{r}}\) | A1cso [5] | Correct completion, no errors, clear notation; candidates using = signs without specifying slipping condition score 4/5 |
# Question 1:
| Working/Answer | Marks | Guidance |
|---|---|---|
| $F \leqslant \mu mg$ or $F = \mu mg$ or $F \leqslant \mu R$ and $R = mg$ or $F = \mu R$ and $R = mg$ | B1 | Award for any of these four statements seen |
| $F = mr\omega^2$ or $F \geq mr\omega^2$ | M1A1 | Equation of motion horizontally; acceleration in either form; can be inequality; must include $F$ |
| $mr\omega^2 \leqslant \mu mg$ | dM1 | Eliminate $F$; must now have an inequality |
| $\omega \leqslant \sqrt{\dfrac{\mu g}{r}}$ | A1cso [5] | Correct completion, no errors, clear notation; candidates using = signs without specifying slipping condition score 4/5 |
---\begin{enumerate}
\item A rough disc is rotating in a horizontal plane with constant angular speed $\omega$ about a vertical axis through the centre of the disc. A particle $P$ is placed on the disc at a distance $r$ from the axis. The coefficient of friction between $P$ and the disc is $\mu$.
\end{enumerate}
Given that $P$ does not slip on the disc, show that
$$\omega \leqslant \sqrt { \frac { \mu g } { r } }$$
\hfill \mbox{\textit{Edexcel M3 2018 Q1 [5]}}