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: $W = C\theta\,$