A-level Mathematics/OCR/M4

This is the Mechanics 4 module of the A-level Mathematics book. This module assumes that you are familiar with the ../C1/, ../C2/, ../C3/, ../C4/, ../M1/, ../M2/ and ../M3/ modules. Please post all questions to A-level Mathematics/Discussion.

Contents

 * 1) /Relative Motion
 * 2) /Centre of Mass (Second Level)/
 * 3) /Moment of Inertia/
 * 4) /Rotation of a Rigid Body/
 * 5) /Simple Harmonic Motion (Second Level)/

Formulae
By the end of this module you will be expected to have learnt the following formulae:

Relative Velocity

 * $${}_P\!V_Q + {}_Q\!V_R = {}_P\!V_R$$

Angular Motion
For constant angular acceleration:
 * $$ \omega _1 = \omega _0 + \alpha t \,$$
 * $$ \theta = \omega _0 t + \frac{1}{2} \alpha t^2$$
 * $$ \theta = \frac{1}{2}(\omega _0 + \omega _1)t$$
 * $$ \omega _1^2 = \omega _0^2 + 2\alpha\theta$$
 * $$ \theta = \omega _1 t - \frac{1}{2} \alpha t^2$$


 * Angular momentum: $$ I\omega\,$$
 * Kinetic energy: $$ \frac{1}{2}I\omega ^2$$
 * Equation of motion: $$ C = I \ddot{\theta}$$
 * Work done by a constant couple: $$ W = C\theta\,$$