A-level Mathematics/OCR/M3

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

1. Elastic Strings and Springs
2. Impulse and Momentum
3. Circular Motion
4. Kinematics
5. Simple Harmonic Motion

Formulae

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

Kinematics

• $a = v\frac{dv}{dx}$

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, $x = a \cos (\omega t + \epsilon)\,$

Elastic Springs and Strings

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

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