Editing Circular motion (section)

==== Acceleration ====
{{main|Acceleration}}

The left-hand circle in Figure 2 is the orbit showing the velocity vectors at two adjacent times. On the right, these two velocities are moved so their tails coincide. Because speed is constant, the velocity vectors on the right sweep out a circle as time advances. For a swept angle {{math|1=''dθ'' = ''ω'' ''dt''}} the change in {{math|'''v'''}} is a vector at right angles to {{math|'''v'''}} and of magnitude {{math|''v'' ''dθ''}}, which in turn means that the magnitude of the acceleration is given by 
<math display="block">a_c = v \frac{d\theta}{dt} = v\omega = \frac{v^2}{r}</math>

{| class="wikitable"
|+ Centripetal acceleration for some values of radius and magnitude of velocity
! colspan="2" rowspan="2" {{diagonal split header 2|{{mvar|r}}|{{math|{{abs|''v''}}}}}} <!-- due to a quirk of the {{diagonal split header}} template don't put a pipe/bar between the colspan/rowspan values and the start of the {{diagonal split header}} template -->
! 1&nbsp;m/s<br />3.6&nbsp;km/h<br />2.2&nbsp;mph
! 2&nbsp;m/s<br />7.2&nbsp;km/h<br />4.5&nbsp;mph
! 5&nbsp;m/s<br />18&nbsp;km/h<br />11&nbsp;mph
! 10&nbsp;m/s<br />36&nbsp;km/h<br />22&nbsp;mph
! 20&nbsp;m/s<br />72&nbsp;km/h<br />45&nbsp;mph
! 50&nbsp;m/s<br />180&nbsp;km/h<br />110&nbsp;mph
! 100&nbsp;m/s<br />360&nbsp;km/h<br />220&nbsp;mph
|-
! Slow [[walk]]
!
! [[Bicycle]]
!
! [[City car]]
!
! [[Aerobatics]]
|-
! 10&nbsp;cm<br />3.9 in
! [[Laboratory centrifuge|Laboratory<br />centrifuge]]
| bgcolor="#ffff99" |10&nbsp;m/s<sup>2</sup><br />1.0 ''g''
| bgcolor="#ffff99" |40&nbsp;m/s<sup>2</sup><br />4.1 ''g''
| bgcolor="#ffddaa" |250&nbsp;m/s<sup>2</sup><br />25 ''g''
| bgcolor="#ffbbbb" |1.0&nbsp;km/s<sup>2</sup><br />100 ''g''
| bgcolor="#ffbbbb" |4.0&nbsp;km/s<sup>2</sup><br />410 ''g''
| bgcolor="#ffccff" |25&nbsp;km/s<sup>2</sup><br />2500 ''g''
| bgcolor="#ff99ff" |100&nbsp;km/s<sup>2</sup><br />10000 ''g''
|-
! 20&nbsp;cm<br />7.9 in
!
| bgcolor="#ccffcc" |5.0&nbsp;m/s<sup>2</sup><br />0.51 ''g''
| bgcolor="#ffff99" |20&nbsp;m/s<sup>2</sup><br />2.0 ''g''
| bgcolor="#ffddaa" |130&nbsp;m/s<sup>2</sup><br />13 ''g''
| bgcolor="#ffddaa" |500&nbsp;m/s<sup>2</sup><br />51 ''g''
| bgcolor="#ffbbbb" |2.0&nbsp;km/s<sup>2</sup><br />200 ''g''
| bgcolor="#ffccff" |13&nbsp;km/s<sup>2</sup><br />1300 ''g''
| bgcolor="#ffccff" |50&nbsp;km/s<sup>2</sup><br />5100 ''g''
|-
! 50&nbsp;cm<br />1.6&nbsp;ft
!
| bgcolor="#ccffcc" |2.0&nbsp;m/s<sup>2</sup><br />0.20 ''g''
| bgcolor="#ccffcc" |8.0&nbsp;m/s<sup>2</sup><br />0.82 ''g''
| bgcolor="#ffff99" |50&nbsp;m/s<sup>2</sup><br />5.1 ''g''
| bgcolor="#ffddaa" |200&nbsp;m/s<sup>2</sup><br />20 ''g''
| bgcolor="#ffddaa" |800&nbsp;m/s<sup>2</sup><br />82 ''g''
| bgcolor="#ffbbbb" |5.0&nbsp;km/s<sup>2</sup><br />510 ''g''
| bgcolor="#ffccff" |20&nbsp;km/s<sup>2</sup><br />2000 ''g''
|-
! 1 m<br />3.3&nbsp;ft
! [[Playground]]<br />[[carousel]]
| bgcolor="#ccffcc" |1.0&nbsp;m/s<sup>2</sup><br />0.10 ''g''
| bgcolor="#ccffcc" |4.0&nbsp;m/s<sup>2</sup><br />0.41 ''g''
| bgcolor="#ffff99" |25&nbsp;m/s<sup>2</sup><br />2.5 ''g''
| bgcolor="#ffddaa" |100&nbsp;m/s<sup>2</sup><br />10 ''g''
| bgcolor="#ffddaa" |400&nbsp;m/s<sup>2</sup><br />41 ''g''
| bgcolor="#ffbbbb" |2.5&nbsp;km/s<sup>2</sup><br />250 ''g''
| bgcolor="#ffccff" |10&nbsp;km/s<sup>2</sup><br />1000 ''g''
|-
! 2 m<br />6.6&nbsp;ft
!
| bgcolor="#99ffff" |500&nbsp;mm/s<sup>2</sup><br />0.051 ''g''
| bgcolor="#ccffcc" |2.0&nbsp;m/s<sup>2</sup><br />0.20 ''g''
| bgcolor="#ffff99" |13&nbsp;m/s<sup>2</sup><br />1.3 ''g''
| bgcolor="#ffff99" |50&nbsp;m/s<sup>2</sup><br />5.1 ''g''
| bgcolor="#ffddaa" |200&nbsp;m/s<sup>2</sup><br />20 ''g''
| bgcolor="#ffbbbb" |1.3&nbsp;km/s<sup>2</sup><br />130 ''g''
| bgcolor="#ffbbbb" |5.0&nbsp;km/s<sup>2</sup><br />510 ''g''
|-
! 5 m<br />16&nbsp;ft
!
| bgcolor="#99ffff" |200&nbsp;mm/s<sup>2</sup><br />0.020 ''g''
| bgcolor="#99ffff" |800&nbsp;mm/s<sup>2</sup><br />0.082 ''g''
| bgcolor="#ccffcc" |5.0&nbsp;m/s<sup>2</sup><br />0.51 ''g''
| bgcolor="#ffff99" |20&nbsp;m/s<sup>2</sup><br />2.0 ''g''
| bgcolor="#ffff99" |80&nbsp;m/s<sup>2</sup><br />8.2 ''g''
| bgcolor="#ffddaa" |500&nbsp;m/s<sup>2</sup><br />51 ''g''
| bgcolor="#ffbbbb" |2.0&nbsp;km/s<sup>2</sup><br />200 ''g''
|-
! 10 m<br />33&nbsp;ft
![[Roller-coaster]]<br />[[vertical loop]]
| bgcolor="#99ffff" |100&nbsp;mm/s<sup>2</sup><br />0.010 ''g''
| bgcolor="#99ffff" |400&nbsp;mm/s<sup>2</sup><br />0.041 ''g''
| bgcolor="#ccffcc" |2.5&nbsp;m/s<sup>2</sup><br />0.25 ''g''
| bgcolor="#ffff99" |10&nbsp;m/s<sup>2</sup><br />1.0 ''g''
| bgcolor="#ffff99" |40&nbsp;m/s<sup>2</sup><br />4.1 ''g''
| bgcolor="#ffddaa" |250&nbsp;m/s<sup>2</sup><br />25 ''g''
| bgcolor="#ffbbbb" |1.0&nbsp;km/s<sup>2</sup><br />100 ''g''
|-
! 20 m<br />66&nbsp;ft
!
| bgcolor="#ddddff" |50&nbsp;mm/s<sup>2</sup><br />0.0051 ''g''
| bgcolor="#99ffff" |200&nbsp;mm/s<sup>2</sup><br />0.020 ''g''
| bgcolor="#ccffcc" |1.3&nbsp;m/s<sup>2</sup><br />0.13 ''g''
| bgcolor="#ccffcc" |5.0&nbsp;m/s<sup>2</sup><br />0.51 ''g''
| bgcolor="#ffff99" |20&nbsp;m/s<sup>2</sup><br />2 ''g''
| bgcolor="#ffddaa" |130&nbsp;m/s<sup>2</sup><br />13 ''g''
| bgcolor="#ffddaa" |500&nbsp;m/s<sup>2</sup><br />51 ''g''
|-
! 50 m<br />160&nbsp;ft
!
| bgcolor="#ddddff" |20&nbsp;mm/s<sup>2</sup><br />0.0020 ''g''
| bgcolor="#ddddff" |80&nbsp;mm/s<sup>2</sup><br />0.0082 ''g''
| bgcolor="#99ffff" |500&nbsp;mm/s<sup>2</sup><br />0.051 ''g''
| bgcolor="#ccffcc" |2.0&nbsp;m/s<sup>2</sup><br />0.20 ''g''
| bgcolor="#ccffcc" |8.0&nbsp;m/s<sup>2</sup><br />0.82 ''g''
| bgcolor="#ffff99" |50&nbsp;m/s<sup>2</sup><br />5.1 ''g''
| bgcolor="#ffddaa" |200&nbsp;m/s<sup>2</sup><br />20 ''g''
|-
! 100 m<br />330&nbsp;ft
! [[Freeway]]<br />[[Entrance ramp|on-ramp]]
| bgcolor="#ddddff" |10&nbsp;mm/s<sup>2</sup><br />0.0010 ''g''
| bgcolor="#ddddff" |40&nbsp;mm/s<sup>2</sup><br />0.0041 ''g''
| bgcolor="#99ffff" |250&nbsp;mm/s<sup>2</sup><br />0.025 ''g''
| bgcolor="#ccffcc" |1.0&nbsp;m/s<sup>2</sup><br />0.10 ''g''
| bgcolor="#ccffcc" |4.0&nbsp;m/s<sup>2</sup><br />0.41 ''g''
| bgcolor="#ffff99" |25&nbsp;m/s<sup>2</sup><br />2.5 ''g''
| bgcolor="#ffddaa" |100&nbsp;m/s<sup>2</sup><br />10 ''g''
|-
! 200 m<br />660&nbsp;ft
!
| bgcolor="#ffffff" |5.0&nbsp;mm/s<sup>2</sup><br />0.00051 ''g''
| bgcolor="#ddddff" |20&nbsp;mm/s<sup>2</sup><br />0.0020 ''g''
| bgcolor="#99ffff" |130&nbsp;m/s<sup>2</sup><br />0.013 ''g''
| bgcolor="#99ffff" |500&nbsp;mm/s<sup>2</sup><br />0.051 ''g''
| bgcolor="#ccffcc" |2.0&nbsp;m/s<sup>2</sup><br />0.20 ''g''
| bgcolor="#ffff99" |13&nbsp;m/s<sup>2</sup><br />1.3 ''g''
| bgcolor="#ffff99" |50&nbsp;m/s<sup>2</sup><br />5.1 ''g''
|-
! 500 m<br />1600&nbsp;ft
!
| bgcolor="#ffffff" |2.0&nbsp;mm/s<sup>2</sup><br />0.00020 ''g''
| bgcolor="#ffffff" |8.0&nbsp;mm/s<sup>2</sup><br />0.00082 ''g''
| bgcolor="#ddddff" |50&nbsp;mm/s<sup>2</sup><br />0.0051 ''g''
| bgcolor="#99ffff" |200&nbsp;mm/s<sup>2</sup><br />0.020 ''g''
| bgcolor="#99ffff" |800&nbsp;mm/s<sup>2</sup><br />0.082 ''g''
| bgcolor="#ccffcc" |5.0&nbsp;m/s<sup>2</sup><br />0.51 ''g''
| bgcolor="#ffff99" |20&nbsp;m/s<sup>2</sup><br />2.0 ''g''
|-
! 1&nbsp;km<br />3300&nbsp;ft
! [[High-speed rail|High-speed<br />railway]]
| bgcolor="#ffffff" |1.0&nbsp;mm/s<sup>2</sup><br />0.00010 ''g''
| bgcolor="#ffffff" |4.0&nbsp;mm/s<sup>2</sup><br />0.00041 ''g''
| bgcolor="#ddddff" |25&nbsp;mm/s<sup>2</sup><br />0.0025 ''g''
| bgcolor="#99ffff" |100&nbsp;mm/s<sup>2</sup><br />0.010 ''g''
| bgcolor="#99ffff" |400&nbsp;mm/s<sup>2</sup><br />0.041 ''g''
| bgcolor="#ccffcc" |2.5&nbsp;m/s<sup>2</sup><br />0.25 ''g''
| bgcolor="#ffff99" |10&nbsp;m/s<sup>2</sup><br />1.0 ''g''
|}