A-level Mathematics/OCR/M2

This is the Mechanics 2 module of the OCR A-level Mathematics book. This module assumes that you are familiar with the C1, C2, C3, C4 and M1 modules. Please post all questions to A-level Mathematics/Discussion.

Contents

1. Centre of Mass
2. Equilibrium of a Rigid Body
3. Projectile Motion
4. Uniform Circular Motion
5. Impulse
6. Work, Energy and Power

Formulae

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

Projectile Motion

• Equation of Trajectory: $y=x\tan \theta -{\frac {gx^{2}}{2V^{2}\cos ^{2}\theta }}$

Work, Energy and Power

• Gravitational Potential Energy (GPE): $E_{p}=mgh\,$
• Kinetic Energy (KE): $E_{k}={\frac {1}{2}}mv^{2}$
• Work done by a force: $W=Fd\cos \alpha \,$
• Power of a moving force: $P=Fv\,$

Collisions

• Newton's Experimental Law: Separation speed $=e\times$ Approach speed
• It follows that the coefficient of restitution, $e={\frac {v_{2}-v_{1}}{u_{1}-u_{2}}}$

Centripetal motion

• Using $F=ma\,$, and $a=r\omega ^{2}\,$ $,F=m\omega ^{2}r\,$
• $a={\frac {v^{2}}{r}}$
• $v=r\omega \,$