# Rotation of a rigid body – Further Maths Paper 2 Mechanics

Candidates should be able to:

• understand and use the definition of the moment of inertia of a system of particles about a fixed axis as $$\displaystyle\sum mr^2$$ and the additive property of moment of inertia for a rigid body composed of several parts (the use of integration to find moments of inertia will not be required);
• use the parallel and perpendicular axes theorems (proofs of these theorems will not be required);
• recall and use the equation of angular motion $$C = I\ddot{\theta}$$ for the motion of a rigid body about a fixed axis (simple cases only, where the moment $$C$$ arises from constant forces such as weights or the tension in a string wrapped around the circumference of a flywheel; knowledge of couples is not included and problems will not involve consideration or calculation of forces acting at the axis of rotation);
• recall and use the formula $$\frac{1}{2} I\omega^2$$ for the kinetic energy of a rigid body rotating about a fixed axis;
• use conservation of energy in solving problems concerning mechanical systems where rotation of a rigid body about a fixed axis is involved.

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