# Momentum

## 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 $n=2\pi r{\frac {mv}{hf}}$ 