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Created the page with an introduction to centrifugal force
'''Centrifugal force''' is a [[Fictitious forces|fictitious force]] found in rotating reference frames that causes objects to accelerate away from the axis of acceleration. An example of centrifugal force in action is the force you feel pushing you outwards on a roundabout. It has the same magnitude as the [[centripetal force]] but points outwards rather than inwards.<ref name=britannica>[https://www.britannica.com/science/centrifugal-force britannica.com]</ref> The other two fictitious forces that exist in rotating frames are the [[Coriolis force|Coriolis]] and Euler forces.
Centrifugal force is used in [[Centrifugation|centrifuges]] in order to simulate very high gravitational field (as high as 1,000,000,000 g).<ref name=britannica/> This is particularly useful for separating liquids into their individual components such as [[blood]].
==Mathematics==
The centrifugal [[force]] of an object with mass m can be expressed in [[vector]] notation as:
:<math>
\vec{F} = -m \vec{\omega} \times {\left( \vec{\omega} \times \vec{r} \right)}
</math>
where <math>\vec{\omega}</math> is the angular velocity of the rotating reference frame and <math>\vec{r}</math> is the position vector of the object.<ref>[http://www.mathpages.com/home/kmath633/kmath633.htm mathpages.com]</ref> The [[cross product]]s mean that this force is always perpendicular to the axis of rotation and radially outwards. For an object performing [[circular motion]], the magnitude of the centrifugal force is:
:<math>
F = m\omega^2 r \sin{\theta}
</math>
which is the same as [[centripetal force]] where θ is the angle between the angular velocity vector and the .
==Centrifugal Force on Earth==
As [[Earth]] rotates about its axis each day, we are all in a rotating frame of reference. This means everyone experiences fictitious forces, including centrifugal force. The most obvious effect of centrifugal force is that it affects the [[Acceleration due to Gravity|acceleration due to gravity]]. The outward centrifugal force causes the effective acceleration due to gravity to be lower near the [[equator]], where centrifugal force is greatest. Mathematically, the effective acceleration due to gravity, g<sub>eff</sub> can be written as:
:<math>
g_{eff}=g-\omega^2 R
</math>
with R being the radius of the Earth. Given the Earth complete one revolution per day, this means g is reduced by 0.00346 m s<sup>-1</sup> or 0.346% at the equator compared to the poles.<ref>[https://www-spof.gsfc.nasa.gov/stargaze/Srotfram1.htm www-spof.gsfc.nasa.gov]</ref> This means that a object [[weight|weighs]] less at the [[equator]] than at the poles.
Centrifugal force also plays a more subtle effect. It causes the equator regions to bulge out and the poles to flattern. This distorts the [[Earth]] from being a [[sphere]] into a squashed sphere known as an "oblate spheroid". This adds to the effect mentioned above as it means a point on Earth's surface is further away from the centre at the equator than at the poles and so g is less there anyway.
==References==
{{reflist}}
==See also==
*[[Fictitious forces]]
*[[Coriolis force]]
*[[Euler force]]
[[Category:Physics]]
[[Category:Mechanics]]
Centrifugal force is used in [[Centrifugation|centrifuges]] in order to simulate very high gravitational field (as high as 1,000,000,000 g).<ref name=britannica/> This is particularly useful for separating liquids into their individual components such as [[blood]].
==Mathematics==
The centrifugal [[force]] of an object with mass m can be expressed in [[vector]] notation as:
:<math>
\vec{F} = -m \vec{\omega} \times {\left( \vec{\omega} \times \vec{r} \right)}
</math>
where <math>\vec{\omega}</math> is the angular velocity of the rotating reference frame and <math>\vec{r}</math> is the position vector of the object.<ref>[http://www.mathpages.com/home/kmath633/kmath633.htm mathpages.com]</ref> The [[cross product]]s mean that this force is always perpendicular to the axis of rotation and radially outwards. For an object performing [[circular motion]], the magnitude of the centrifugal force is:
:<math>
F = m\omega^2 r \sin{\theta}
</math>
which is the same as [[centripetal force]] where θ is the angle between the angular velocity vector and the .
==Centrifugal Force on Earth==
As [[Earth]] rotates about its axis each day, we are all in a rotating frame of reference. This means everyone experiences fictitious forces, including centrifugal force. The most obvious effect of centrifugal force is that it affects the [[Acceleration due to Gravity|acceleration due to gravity]]. The outward centrifugal force causes the effective acceleration due to gravity to be lower near the [[equator]], where centrifugal force is greatest. Mathematically, the effective acceleration due to gravity, g<sub>eff</sub> can be written as:
:<math>
g_{eff}=g-\omega^2 R
</math>
with R being the radius of the Earth. Given the Earth complete one revolution per day, this means g is reduced by 0.00346 m s<sup>-1</sup> or 0.346% at the equator compared to the poles.<ref>[https://www-spof.gsfc.nasa.gov/stargaze/Srotfram1.htm www-spof.gsfc.nasa.gov]</ref> This means that a object [[weight|weighs]] less at the [[equator]] than at the poles.
Centrifugal force also plays a more subtle effect. It causes the equator regions to bulge out and the poles to flattern. This distorts the [[Earth]] from being a [[sphere]] into a squashed sphere known as an "oblate spheroid". This adds to the effect mentioned above as it means a point on Earth's surface is further away from the centre at the equator than at the poles and so g is less there anyway.
==References==
{{reflist}}
==See also==
*[[Fictitious forces]]
*[[Coriolis force]]
*[[Euler force]]
[[Category:Physics]]
[[Category:Mechanics]]