A-level Mathematics/OCR/M4

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.

Contents

1. /Relative MotionTemplate:Stage short
2. /Centre of Mass (Second Level)/Template:Stage short
3. /Moment of Inertia/Template:Stage short
4. /Rotation of a Rigid Body/Template:Stage short
5. /Simple Harmonic Motion (Second Level)/Template:Stage short

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: $W=C\theta$