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: $$y = x \tan \theta - \frac {g x^2}{2 V^2 \cos ^2 \theta} $$

Work, Energy and Power

 * Gravitational Potential Energy (GPE): $$E_p = m g h\,$$
 * Kinetic Energy (KE): $$ E_k = \frac{1}{2} mv^2 $$
 * Work done by a force: $$ W = F d\cos \alpha \,$$
 * 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 $$a=r\omega^2\,$$ $$, F=m\omega^2r\,$$
 * $$a=\frac{v^2}{r}$$
 * $$v=r\omega\,$$