| Exam Board | CAIE |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Year | 2010 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circular Motion 1 |
| Type | Radial and transverse acceleration |
| Difficulty | Standard +0.8 This is a Further Maths mechanics question requiring understanding of no-slip conditions, angular kinematics with time-varying angular velocity, and decomposition of acceleration into radial and tangential components. While the individual concepts are standard (ω₁r₁ = ω₂r₂, a_radial = ω²r, a_tangential = αr), students must correctly differentiate to find angular acceleration, apply Pythagoras for magnitude, and use trigonometry for the angle—a multi-step problem requiring careful coordination of several techniques beyond typical A-level. |
| Spec | 6.05a Angular velocity: definitions6.05b Circular motion: v=r*omega and a=v^2/r6.05e Radial/tangential acceleration |
| Answer | Marks |
|---|---|
| (ii) | Equate tangential speeds to find ω : 0⋅5ω = 0⋅3ω , ω = 5/3 [rad s -1 ] M1 A1 |
| Answer | Marks | Guidance |
|---|---|---|
| = 0⋅464 rad or 26⋅6° A1 | 2 | |
| 7 | [9] | |
| Page 5 | Mark Scheme: Teachers’ version | Syllabus |
| GCE A LEVEL – May/June 2010 | 9231 | 22 |
Question 4:
--- 4 (i)
(ii) ---
4 (i)
(ii) | Equate tangential speeds to find ω : 0⋅5ω = 0⋅3ω , ω = 5/3 [rad s -1 ] M1 A1
B A B B
Find tangential acceleration, r d 2θ/dt 2 : 0⋅5 × ½ = 0⋅25 M1 A1
Find radial acceleration, r (dθ/dt) 2 : 0⋅5 × 1 2 = 0⋅5 B1
Combine to give mag. of acceln: √(0⋅25 2 + 0⋅5 2 ) M1
= √5/4 or 0⋅559 [m s -2 ] A1
Find angle made with PA (A.E.F.): tan -1 (0⋅25/0⋅5) M1
= 0⋅464 rad or 26⋅6° A1 | 2
7 | [9]
Page 5 | Mark Scheme: Teachers’ version | Syllabus | Paper
GCE A LEVEL – May/June 2010 | 9231 | 22\includegraphics{figure_4}
Two coplanar discs, of radii $0.5$ m and $0.3$ m, rotate about their centres $A$ and $B$ respectively, where $AB = 0.8$ m. At time $t$ seconds the angular speed of the larger disc is $\frac{1}{2}t$ rad s$^{-1}$ (see diagram). There is no slipping at the point of contact. For the instant when $t = 2$, find
\begin{enumerate}[label=(\roman*)]
\item the angular speed of the smaller disc, [2]
\item the magnitude of the acceleration of a point $P$ on the circumference of the larger disc, and the angle between the direction of this acceleration and $PA$. [7]
\end{enumerate}
\hfill \mbox{\textit{CAIE FP2 2010 Q4 [9]}}