| Exam Board | OCR |
|---|---|
| Module | M4 (Mechanics 4) |
| Year | 2015 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circular Motion 1 |
| Type | Angular kinematics – constant angular acceleration/deceleration |
| Difficulty | Moderate -0.8 This is a straightforward application of constant angular acceleration equations (rotational analogues of SUVAT). Students need to convert 4 revolutions to radians, then apply standard kinematic formulas with no conceptual difficulty or problem-solving required—purely mechanical substitution into familiar equations. |
| Spec | 3.02d Constant acceleration: SUVAT formulae6.05a Angular velocity: definitions6.05b Circular motion: v=r*omega and a=v^2/r |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| 4 revolutions \(\Rightarrow \theta = 8\pi\) | B1 | |
| \(12.4^2 = 3^2 + 2\alpha(8\pi)\) | M1 | Using \(\omega^2 = \omega_0^2 + 2\alpha\theta\) with \(\text{cv}(\theta \neq 4)\) |
| \(\alpha = 2.88\) rad s\(^{-2}\) (3 s f) | A1 [3] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(8\pi = \frac{1}{2}(3 + 12.4)t\) | M1 | Using \(\theta = \frac{1}{2}(\omega_0 + \omega)t\) with \(\text{cv}(\theta)\) (allow any \(\theta\)) |
| \(t = 3.26\) s (3 s f) | A1 [2] |
# Question 1:
## Part (i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| 4 revolutions $\Rightarrow \theta = 8\pi$ | B1 | |
| $12.4^2 = 3^2 + 2\alpha(8\pi)$ | M1 | Using $\omega^2 = \omega_0^2 + 2\alpha\theta$ with $\text{cv}(\theta \neq 4)$ |
| $\alpha = 2.88$ rad s$^{-2}$ (3 s f) | A1 **[3]** | |
## Part (ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $8\pi = \frac{1}{2}(3 + 12.4)t$ | M1 | Using $\theta = \frac{1}{2}(\omega_0 + \omega)t$ with $\text{cv}(\theta)$ (allow any $\theta$) |
| $t = 3.26$ s (3 s f) | A1 **[2]** | |
---1 A turntable is rotating at $3 \mathrm { rad } \mathrm { s } ^ { - 1 }$. The turntable is then accelerated so that after 4 revolutions it is rotating at $12.4 \mathrm { rad } \mathrm { s } ^ { - 1 }$. Assuming that the angular acceleration of the turntable is constant,\\
(i) find the angular acceleration,\\
(ii) find the time taken to increase its angular speed from $3 \mathrm { rad } \mathrm { s } ^ { - 1 }$ to $12.4 \mathrm { rad } \mathrm { s } ^ { - 1 }$.
\hfill \mbox{\textit{OCR M4 2015 Q1 [5]}}