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

 Dynamics $P=\,m.v$ Momentum is mass times velocity. $F={\frac {dP}{dt}}$ 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. $x=A\sin \left(2\pi ft\right)$ Displacement from the centre of oscillation is amplitude times position in cycle. (When oscillation started at centre). $x=A\cos \left(2\pi ft\right)$ 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 ($\mathbf {6.67\times 10^{-11}Nm^{2}kg^{-2}}$ ) times mass one times mass two over radius squared.