| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9795/2 (Pre-U Further Mathematics Paper 2) |
| Year | 2017 |
| Session | June |
| Marks | 5 |
| Topic | Circular Motion 1 |
| Type | Radial and transverse acceleration |
| Difficulty | Moderate -0.3 This is a straightforward application of standard circular motion formulas. Part (i) uses basic constant angular acceleration kinematics (ω = ω₀ + αt), while part (ii) requires direct substitution into the formulas for radial acceleration (rω²) and transverse acceleration (rα). The calculations are routine with no conceptual challenges or problem-solving required, making it slightly easier than average but still requiring correct formula recall and execution. |
| Spec | 6.05a Angular velocity: definitions6.05e Radial/tangential acceleration |
| Answer | Marks | Guidance |
|---|---|---|
| \( | \mathbf{a} | = \sqrt{(0.63^2 + 0.216^2)}\) M1 Find |
Total: 5 marks
**Part (i):**
$\dot{\omega} = 4.2$ **B1**
**Part (ii):**
$r\dot{\omega} = 0.63$ **B1** $r\dot{\omega}$ seen
$r\omega^2 = \pm 0.216$ **B1** $r\omega^2$ seen
$|\mathbf{a}| = \sqrt{(0.63^2 + 0.216^2)}$ **M1** Find |acceleration| for stated components
$= 0.666$ **A1** Answer, a.r.t. 0.666
Total: **5 marks**8 A horizontal turntable rotates about a vertical axis. Starting from rest, it accelerates uniformly to an angular velocity of $8.4 \mathrm { rad } \mathrm { s } ^ { - 1 }$ in 2 s .\\
(i) Find the angular acceleration of the turntable.\\
(ii) A particle rests on the turntable at a distance of 0.15 m from the axis. Find the radial and transverse components of the acceleration of the particle when the angular velocity is $1.2 \mathrm { rad } \mathrm { s } ^ { - 1 }$. Find also the magnitude of the acceleration at this instant.
\hfill \mbox{\textit{Pre-U Pre-U 9795/2 2017 Q8 [5]}}