A-level Mathematics/OCR/M4

From Wikibooks, the open-content textbooks collection

Jump to: navigation, search

Please post all questions to A-level_Mathematics/Discussion

Contents

[edit] Introduction

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

[edit] Contents

  1. Relative MotionDevelopment stage: 00% (as of Dec 14, 2005)
  2. Centre of Mass(Second Level)Development stage: 00% (as of Dec 14, 2005)
  3. Moment of InertiaDevelopment stage: 00% (as of Dec 14, 2005)
  4. Rotation of a Rigid BodyDevelopment stage: 00% (as of Dec 14, 2005)
  5. Simple Harmonic Motion(Second Level)Development stage: 00% (as of Dec 14, 2005)

[edit] Formulae

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

[edit] Relative Velocity

  • {}_P\!V_Q + {}_Q\!V_R = {}_P\!V_R

[edit] 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\,
Retrieved from "http://en.wikibooks.org/wiki/A-level_Mathematics/OCR/M4"