# 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.

## Formulae

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

### Relative Velocity

• ${\displaystyle {}_{P}\!V_{Q}+{}_{Q}\!V_{R}={}_{P}\!V_{R}}$

### Angular Motion

For constant angular acceleration:

• ${\displaystyle \omega _{1}=\omega _{0}+\alpha t\,}$
• ${\displaystyle \theta =\omega _{0}t+{\frac {1}{2}}\alpha t^{2}}$
• ${\displaystyle \theta ={\frac {1}{2}}(\omega _{0}+\omega _{1})t}$
• ${\displaystyle \omega _{1}^{2}=\omega _{0}^{2}+2\alpha \theta }$
• ${\displaystyle \theta =\omega _{1}t-{\frac {1}{2}}\alpha t^{2}}$
• Angular momentum: ${\displaystyle I\omega \,}$
• Kinetic energy: ${\displaystyle {\frac {1}{2}}I\omega ^{2}}$
• Equation of motion: ${\displaystyle C=I{\ddot {\theta }}}$
• Work done by a constant couple: ${\displaystyle W=C\theta \,}$