A-level Mathematics/OCR/M3

Please post all questions to A-level_Mathematics/Discussion

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

Contents

1. Elastic Strings and SpringsTemplate:Stage short
2. Impulse and MomentumTemplate:Stage short
3. Circular MotionTemplate:Stage short
4. KinematicsTemplate:Stage short
5. Simple Harmonic MotionTemplate:Stage short

Formulae

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

Kinematics

• $a=v\frac{dv}{ds}$

Simple Harmonic Motion

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

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 $\theta$ is in radians