| Exam Board | OCR |
|---|---|
| Module | M4 (Mechanics 4) |
| Year | 2011 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circular Motion 1 |
| Type | Angular kinematics – constant angular acceleration/deceleration |
| Difficulty | Moderate -0.3 This is a straightforward application of constant angular acceleration equations (rotational analogues of SUVAT). All three parts require direct substitution into standard formulae with no problem-solving insight needed. Part (iii) requires slightly more care in converting revolutions to radians and working backwards from rest, but remains routine for M4 students. Slightly easier than average due to its mechanical nature. |
| Spec | 6.05a Angular velocity: definitions |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Using \(\omega_2 = \omega_1 + \alpha t\), \(750 = 950 - 0.8t\) | M1 | |
| Time taken is 250 s | A1 | |
| [2] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Using \(\omega_2^2 = \omega_1^2 + 2\alpha\theta\), \(200^2 = 220^2 - 1.6\theta\) | M1 | |
| Angle is 5250 rad | A1 | |
| [2] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Angle is \(20\pi\) rad | B1 | |
| Using \(\theta = \omega_2 t - \frac{1}{2}\alpha t^2\), \(20\pi = 0 + 0.4t^2\) | M1 | Or equivalent; e.g. finding \(\omega_1 = 10.03\) and then \(t = \omega_1 \div 0.8\) |
| Time taken is 12.5 s (3 sf) | A1 | Accept \(\sqrt{50\pi}\) or \(5\sqrt{2\pi}\) |
| [3] |
# Question 1:
## Part (i)
| Answer/Working | Marks | Guidance |
|---|---|---|
| Using $\omega_2 = \omega_1 + \alpha t$, $750 = 950 - 0.8t$ | M1 | |
| Time taken is 250 s | A1 | |
| | [2] | |
## Part (ii)
| Answer/Working | Marks | Guidance |
|---|---|---|
| Using $\omega_2^2 = \omega_1^2 + 2\alpha\theta$, $200^2 = 220^2 - 1.6\theta$ | M1 | |
| Angle is 5250 rad | A1 | |
| | [2] | |
## Part (iii)
| Answer/Working | Marks | Guidance |
|---|---|---|
| Angle is $20\pi$ rad | B1 | |
| Using $\theta = \omega_2 t - \frac{1}{2}\alpha t^2$, $20\pi = 0 + 0.4t^2$ | M1 | Or equivalent; e.g. finding $\omega_1 = 10.03$ and then $t = \omega_1 \div 0.8$ |
| Time taken is 12.5 s (3 sf) | A1 | Accept $\sqrt{50\pi}$ or $5\sqrt{2\pi}$ |
| | [3] | |
---1 When the power is turned off, a fan disk inside a jet engine slows down with constant angular deceleration $0.8 \mathrm { rad } \mathrm { s } ^ { - 2 }$.\\
(i) Find the time taken for the angular speed to decrease from $950 \mathrm { rad } \mathrm { s } ^ { - 1 }$ to $750 \mathrm { rad } \mathrm { s } ^ { - 1 }$.\\
(ii) Find the angle through which the disk turns as the angular speed decreases from $220 \mathrm { rad } \mathrm { s } ^ { - 1 }$ to $200 \mathrm { rad } \mathrm { s } ^ { - 1 }$.\\
(iii) Find the time taken for the disk to make the final 10 revolutions before coming to rest.
\hfill \mbox{\textit{OCR M4 2011 Q1 [7]}}