# 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

${\displaystyle p=mv}$

For any motion, the interaction force is

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

In general

${\displaystyle p=mv=Ft}$

## Application

### Momentum of a Mass

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

### Momentum of a Relativistic Mass

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

### Momentum of a Massless Quanta

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

### Momentum of Electric charge in circle

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

### Momentum of Atom's Free Electron

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

### Momentum of Atom's Bind Electron

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