# Fundamental Physics/Motion/Circular motion

Circular motion represents motion around a circle or an arc of a circle

## Complete Circular motion

 Distance ${\displaystyle s}$ ${\displaystyle 2\pi r}$ Time ${\displaystyle t}$ ${\displaystyle t}$ Speed ${\displaystyle v}$ ${\displaystyle r{\frac {2\pi }{t}}=r\omega }$ Acceleration ${\displaystyle a}$ ${\displaystyle {\frac {r\omega }{t}}}$ Force ${\displaystyle F}$ ${\displaystyle m{\frac {r\omega }{t}}}$ Work ${\displaystyle W}$ ${\displaystyle pr\omega }$ Energy ${\displaystyle E}$ ${\displaystyle {\frac {pr\omega }{t}}}$ Angular speed ${\displaystyle \omega }$ ${\displaystyle 2\pi f}$ Frequency ${\displaystyle f}$ ${\displaystyle {\frac {1}{t}}}$

## Circular arc motion

Circular motion of non-constant acceleration . Example, circular motion of arc of circle

${\displaystyle s=r\theta }$
${\displaystyle v={\frac {ds}{dt}}={\frac {ds}{dt}}r\theta =r{\frac {d\theta }{dt}}=r\omega }$
${\displaystyle a={\frac {dv}{dt}}={\frac {d}{dt}}r\omega =r{\frac {d\omega }{dt}}=r\alpha }$

 Distance ${\displaystyle s}$ ${\displaystyle \theta r}$ Time ${\displaystyle t}$ ${\displaystyle t}$ Speed ${\displaystyle v}$ ${\displaystyle r{\frac {\theta }{t}}=v\omega }$ Acceleration ${\displaystyle a}$ ${\displaystyle {\frac {v^{2}}{r}}}$ Force ${\displaystyle F}$ ${\displaystyle m{\frac {v^{2}}{r}}}$ Work ${\displaystyle W}$ ${\displaystyle p{\frac {v^{2}}{r}}}$ Energy ${\displaystyle E}$ ${\displaystyle p{\frac {v^{2}}{rt}}}$ Angular speed ${\displaystyle \omega }$ ${\displaystyle \theta f}$ Frequency ${\displaystyle f}$ ${\displaystyle {\frac {1}{t}}}$