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

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