structural:summarization
Rotating sphere

Consider a location with latitude φ on a sphere that is rotating around the north–south axis. A local coordinate system is set up with the x axis horizontally due east, the y axis horizontally due north and the z axis vertically upwards. The rotation vector, velocity of movement and Coriolis acceleration expressed in this local coordinate system (listing components in the order east (e), north (n) and upward (u)) are:

When considering atmospheric or oceanic dynamics, the vertical velocity is small, and the vertical component of the Coriolis acceleration (v e cos φ {\displaystyle v_{e}\cos \varphi }) is small compared with the acceleration due to gravity (g, approximately 9.81 m/s (32.2 ft/s) near Earth's surface). For such cases, only the horizontal (east and north) components matter. The restriction of the above to the horizontal plane is (setting v = 0):

where f = 2 ω sin φ {\displaystyle f=2\omega \sin \varphi \,} is called the Coriolis parameter.

By setting v = 0, it can be seen immediately that (for positive φ and ω) a movement due east results in an acceleration due south; similarly, setting v = 0, it is seen that a movement due north results in an acceleration due east. In general, observed horizontally, looking along the direction of the movement causing the acceleration, the acceleration always is turned 90° to the right (for positive φ) and of the same size regardless of the horizontal orientation.

In the case of equatorial motion, setting φ = 0° yields:

Ω in this case is parallel to the north axis.

Accordingly, an eastward motion (that is, in the same direction as the rotation of the sphere) provides an upward acceleration known as the Eötvös effect, and an upward motion produces an acceleration due west.