| Exam Board | CAIE |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Year | 2018 |
| Session | June |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments of inertia |
| Type | Find unknown parameter from period |
| Difficulty | Challenging +1.8 This is a challenging Further Maths mechanics problem requiring calculation of moment of inertia for a composite body using parallel axis theorem, then applying energy conservation with rotational motion. Part (i) involves systematic application of standard formulas but with careful geometry. Part (ii) requires setting up and solving an energy equation involving the given angular speed. The multi-step nature, composite geometry, and integration of multiple concepts (moments of inertia, rotational energy, potential energy) make this significantly harder than average, though it follows a structured approach once the method is identified. |
| Spec | 6.04e Rigid body equilibrium: coplanar forces |
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An object is formed from a square frame $A B C D$ with a square lamina attached in one corner of the frame. The frame consists of four identical thin rods, each of mass $M$ and length $2 a$. The lamina has mass $k M$ and edges of length $a$. It has one vertex at $C$ and adjacent sides in contact with $C B$ and $C D$ (see diagram).\\
(i) Show that the moment of inertia of the object about an axis $l$ through $A$ perpendicular to the plane of the object is $\frac { 2 } { 3 } M a ^ { 2 } ( 7 k + 20 )$.\\
The object is released from rest with the edge $A B$ horizontal and $D$ vertically above $A$. The object rotates freely about the fixed axis $l$. The angular speed of the object is $\frac { 1 } { 2 } \sqrt { } \left( \frac { 5 g } { a } \right)$ when $D$ is first vertically below $A$.\\
(ii) Find the value of $k$.\\
\hfill \mbox{\textit{CAIE FP2 2018 Q11 EITHER}}