A-level Mathematics/OCR/M3

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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.

Contents[edit]

  1. Elastic Strings and Springs75% developed  as of Dec 14, 2005
  2. Impulse and Momentum0% developed  as of Dec 14, 2005
  3. Circular Motion75% developed  as of Dec 14, 2005
  4. Kinematics0% developed  as of Dec 14, 2005
  5. Simple Harmonic Motion100% developed  as of Dec 14, 2005

Formulae[edit]

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

Kinematics[edit]

  •  a = v\frac{dv}{dx}

Simple Harmonic Motion[edit]

  • \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)\,

Elastic Springs and Strings[edit]

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

Small-angle Approximations[edit]

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

only applies when  \theta is in radians