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: $W=C\theta \,$