| Exam Board | CAIE |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Year | 2019 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Topic | Moments of inertia |
| Type | Find unknown parameter from period |
| Difficulty | Challenging +1.3 This is a standard compound pendulum problem requiring moment of inertia calculation and energy conservation. While it involves Further Maths content (rotational dynamics), the solution follows a well-established method: calculate I about the pivot using parallel axis theorem, then apply conservation of energy between release and maximum angular speed. The multi-step nature and Further Maths topic place it above average difficulty, but it's a textbook application without requiring novel insight. |
| Spec | 6.04a Centre of mass: gravitational effect6.05a Angular velocity: definitions |
(i) Find the moment of inertia of the object, consisting of the rod and two spheres, about $L$.\\
The object is pivoted at $A$ so that it can rotate freely about $L$. The object is released from rest with the rod making an angle of $60 ^ { \circ }$ to the downward vertical. The greatest angular speed attained by the object in the subsequent motion is $\frac { 9 } { 20 } \sqrt { } \left( \frac { g } { a } \right)$.\\
(ii) Find the value of $k$.\\
\hfill \mbox{\textit{CAIE FP2 2019 Q4 [11]}}