Centrifugal force
In a frame rotating with angular velocity , a particle at position feels the centrifugal force , which points away from the axis of rotation with magnitude .
Consider a hanging string on the Earth.
Rather than hanging vertically downwards, the pendulum hangs at an angle to the vertical. We wish to find .
The forces acting on the particle satisfy
[The string is short compared to , so it does not matter whether we use at the top or the bottom of the string.]
To hold the string together, there must be a force exerted by the molecules on the string that balances the other forces, which is the tension.
The net force on the particle is zero, so
We have 2 equations (for and ) and 2 unknowns ( and ), so we can solve for :
At the equator (), the gravity is a bit weaker, but .
When , , so the effect is very small.
Force and potential
In a frame rotating with angular velocity , a particle at position experiences the centrifugal force
which points away from the axis of rotation. Its size is
where is the distance from the centre of the Earth and is the angle between and the equatorial plane.
The centrifugal force is conservative:
so potential energy is lowered by moving away from the axis of rotation.
Related
Stated in
- Example 6.1 (Hanging String)§6.2 Centrifugal Force