# Centrifugal force

Centrifugal force is a 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. The other two fictitious forces that exist in rotating frames are the Coriolis and Euler forces.

Centrifugal force is used in centrifuges in order to simulate very high gravitational field (as high as 1,000,000,000 g). 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: where is the angular velocity of the rotating reference frame and is the position vector of the object. The cross products 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: 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. 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, geff can be written as: 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−1 or 0.346% at the equator compared to the poles. This means that an object 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.