A-level Mathematics/OCR/M4

< A-level Mathematics < OCR

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.

/Relative Motion
Centre of Mass (Second Level)
Moment of Inertia
Rotation of a Rigid Body
Simple Harmonic Motion (Second Level)

Formulae

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

Relative Velocity

${}_{P}\!V_{Q}+{}_{Q}\!V_{R}={}_{P}\!V_{R}$

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: $W=C\theta \,$

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A-level Mathematics/OCR/M4

Contents

Formulae

Relative Velocity

Angular Motion