CAIE FP2 2019 June — Question 4 11 marks

Exam BoardCAIE
ModuleFP2 (Further Pure Mathematics 2)
Year2019
SessionJune
Marks11
PaperDownload PDF ↗
TopicMoments of inertia
TypeFind unknown parameter from period
DifficultyChallenging +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.
Spec6.04a Centre of mass: gravitational effect6.05a Angular velocity: definitions

  1. 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 \(\frac { 9 } { 20 } \sqrt { } \left( \frac { g } { a } \right)\).
  2. Find the value of \(k\).

(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]}}