Edexcel M3 2009 January — Question 3 7 marks

Exam BoardEdexcel
ModuleM3 (Mechanics 3)
Year2009
SessionJanuary
Marks7
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TopicCircular Motion 1
TypeRotating disc with friction
DifficultyModerate -0.3 This is a straightforward application of circular motion with friction. Students need to convert rpm to rad/s, apply F=mrω², set friction equal to centripetal force, and solve for μ. It's slightly easier than average because it's a direct single-concept problem with clear steps and no geometric complications or proof required.
Spec3.03t Coefficient of friction: F <= mu*R model6.05c Horizontal circles: conical pendulum, banked tracks
3. A rough disc rotates about its centre in a horizontal plane with constant angular speed 80 revolutions per minute. A particle \(P\) lies on the disc at a distance 8 cm from the centre of the disc. The coefficient of friction between \(P\) and the disc is \(\mu\). Given that \(P\) remains at rest relative to the disc, find the least possible value of \(\mu\).
Question 3:
AnswerMarks Guidance
Working/AnswerMarks Guidance
\(\omega = \frac{80 \times 2\pi}{60} \text{ rad s}^{-1} \left(= \frac{8\pi}{3} \approx 8.377...\right)\)B1 Accept \(v = \frac{16\pi}{75} \approx 0.67 \text{ ms}^{-1}\) as equivalent
\((\uparrow)\quad R = mg\)B1
For least \(\mu\): \((\leftarrow)\quad \mu mg = mr\omega^2\)M1 A1=A1
\(\mu = \frac{0.08}{9.8} \times \left(\frac{8\pi}{3}\right)^2 \approx 0.57\)M1 A1 accept 0.573 (7) [7] 
## Question 3:

| Working/Answer | Marks | Guidance |
|---|---|---|
| $\omega = \frac{80 \times 2\pi}{60} \text{ rad s}^{-1} \left(= \frac{8\pi}{3} \approx 8.377...\right)$ | B1 | Accept $v = \frac{16\pi}{75} \approx 0.67 \text{ ms}^{-1}$ as equivalent |
| $(\uparrow)\quad R = mg$ | B1 | |
| For least $\mu$: $(\leftarrow)\quad \mu mg = mr\omega^2$ | M1 A1=A1 | |
| $\mu = \frac{0.08}{9.8} \times \left(\frac{8\pi}{3}\right)^2 \approx 0.57$ | M1 A1 | accept 0.573 **(7) [7]** |

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3. A rough disc rotates about its centre in a horizontal plane with constant angular speed 80 revolutions per minute. A particle $P$ lies on the disc at a distance 8 cm from the centre of the disc. The coefficient of friction between $P$ and the disc is $\mu$. Given that $P$ remains at rest relative to the disc, find the least possible value of $\mu$.\\

\hfill \mbox{\textit{Edexcel M3 2009 Q3 [7]}}
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Q1 7 Q2 9 Q3 7 Q4 11 Q5 12 Q6 14 Q7 15