EXERCISE

This closing exercise set tests every idea developed across the unit, in five question formats:

• Multiple-choice questions probe conceptual traps and quick calculations across the whole chapter — what center of mass does and does not depend on, the turning effect of a couple, conservation of angular momentum in colliding discs, and the racing order of different shapes rolling down an incline.
• Short-answer questions ask for precise definitions and short derivations — center of mass, torque, equilibrium, couple, the principle of moments, center of gravity, moment of inertia, radius of gyration, conservation of angular momentum, and the condition for pure rolling.
• Long-answer questions require full derivations and proofs — the types of equilibrium, finding the center of gravity of an irregular lamina, the bending of a cyclist on a curve, the moment of inertia of a rod/ring/disc from first principles, conservation of angular momentum, the parallel and perpendicular axis theorems, and rolling on an inclined plane.
• Conceptual questions test qualitative understanding without heavy calculation — why a porter leans forward, why a meter scale balances more easily than a match stick, and why a couple cannot be replaced by a single equivalent force. …