# A-level Physics/Forces, Fields and Energy/Appendix of Formulae

 Dynamics $P =\,m.v$ Momentum is mass times velocity. $F = \frac{ d P }{dt}$ Force is the rate of change of momentum with respect to time. Work and Energy $W =\,F.s$ Work is force times displacement $E_k = \frac{1}{2} mv^2$ Kinetic energy is half of mass times velocity squared. $E_p =\,mgh$ Potential energy is mass times acceleration due to gravity times height. (For situations near the surface of the earth only) Circular Motion $a = \frac {v^2}{r}$ Centripetal acceleration is velocity squared divided by the radius. $F = \frac {mv^2}{r}$ Centripetal force is mass times velocity squared divided by the radius. (You are expected to be able to derive this from $F = m.a$ and $a = \frac {v^2}{r}$ ). Oscillations $T = \frac{1}{f}$ Period is one over the frequency. $a = -\left(2\pi f\right)^2 x$ Acceleration is proportional to the negative displacement from the centre of oscillation. $x = A\sin \left(2\pi f t \right)$ Displacement from the centre of oscillation is amplitude times position in cycle. (When oscillation started at centre). $x = A\cos \left( 2\pi f t \right)$ Displacement from the centre of oscillation is amplitude times position in cycle. (When oscillation started at one end). $w = \frac{2 \pi}{T}$ Angular Velocity is 2 times $\pi$ over the time period. $w = \left(2\pi f \right)$ Angular Velocity is 2 times $\pi$ times the frequency of oscillations. Gravitational Fields $F = \frac{Gm_1 m_2}{r^2}$ Force is Gravitational Force Constant ($\mathbf{6.67 \times 10^{-11} N m^2 kg^{-2}}$) times mass one times mass two over radius squared.