A-level Mathematics/OCR/M3

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Please post all questions to A-level_Mathematics/Discussion

Contents

[edit] Introduction

This is the Mechanics 3 module of the A-level Mathematics Book. This module assumes that you are familiar with the C1, C2, C3, C4, M1 and M2 modules. Please post all questions to A-level_Mathematics/Discussion

[edit] Contents

  1. Elastic Strings and SpringsDevelopment stage: 75% (as of Dec 14, 2005)
  2. Impulse and MomentumDevelopment stage: 00% (as of Dec 14, 2005)
  3. Circular MotionDevelopment stage: 75% (as of Dec 14, 2005)
  4. KinematicsDevelopment stage: 00% (as of Dec 14, 2005)
  5. Simple Harmonic MotionDevelopment stage: 100% (as of Dec 14, 2005)

[edit] Formulae

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

[edit] Kinematics

  • a = v\frac{dv}{ds}

[edit] Simple Harmonic Motion

  • \ddot{x} = -\omega ^2x
  • v^2 = \omega ^2(a^2-x^2)\,
  • T = \frac{2\pi}{\omega}
  • x = a \sin (\omega t)\, or x = a \cos (\omega t)\, or, generally, x = a \cos (\omega t + \epsilon)\,

[edit] Elastic Springs and Strings

  • Hooke's Law: T = \frac{\lambda x}{l}
  • Elastic potential energy: E_p = \frac{\lambda x^2}{2l}

[edit] Small-angle Approximations

  • \sin \theta \approx \theta
  • \cos \theta \approx 1 - \frac{1}{2}\theta ^2
  • \tan \theta \approx \theta

only applies when θ is in radians

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