Momentum

Momentum is defined as the movement of a mass at a speed . Momentum is chracterised by its moment which is the product of a mass multiply by its speed . Moment is denoted as p measured in Kg m/s or in Newton N

Moment

p=mv

For any motion, the interaction force is

F=ma=m{\frac {v}{t}}={\frac {p}{t}}

In general

p=mv=Ft

Application

Momentum of a Mass

Speed	$v$	$v$
Mass	$m$	$m$
Momentum	$p$	$mv=Ft$
Force	$F$	$ma=m{\frac {v}{t}}={\frac {p}{t}}$
Work	$W$	$Fs=Fvt=pv$
Energy	$E$	$Fv=Fat=pa$

Momentum of a Relativistic Mass

Speed	$v$	$\gamma ={\sqrt {1-{\frac {v^{2}}{C^{2}}}}}$
Mass	$m$	$m_{o}(\gamma -1)$
Momentum	$p$	$mv$
Energy	$E$	$pv$

Momentum of a Massless Quanta

Speed	$v$	$C=\lambda f$
Mass	$m$	$h=p\lambda$
Energy	$E$	$pv=pC=p\lambda f=hf$
Momentum	$p$	${\frac {h}{\lambda }}$
Wavelength	$\lambda$	${\frac {h}{p}}={\frac {C}{f}}$

Momentum of Electric charge in circle

Equilibrium	$QvB=mv{\frac {v}{r}}$
Speed	$v={\frac {Q}{m}}Br$
Radius	$r={\frac {mv}{QB}}$

Momentum of Atom's Free Electron

Equilibrium	$hf=hf_{o}+{\frac {1}{2}}mv^{2}$
Speed	$v={\sqrt {{\frac {2}{m}}(hf-hf_{o})}}={\sqrt {{\frac {2}{m}}(nhf_{o})}}$ With $f>f_{o}=nf_{o}$ to have $v>0$

Momentum of Atom's Bind Electron

Equilibrium	$nhf=mvr2\pi$
Speed	$v={\frac {1}{2\pi }}{\frac {nhf}{mr}}$
Radius	$r={\frac {1}{2\pi }}{\frac {nhf}{mv}}$
Potential Energy Level n	$n=2\pi r{\frac {mv}{hf}}$

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