ac = -2Ω × v
where:
* ac is the Coriolis acceleration vector
* Ω is the angular velocity vector of the rotating frame of reference (Earth's rotation in this case)
* v is the velocity vector of the object in the rotating frame of reference
Explanation:
* Angular Velocity (Ω): Earth rotates at a rate of approximately 7.2921 × 10-5 radians per second. This value is represented by the vector Ω, which points towards the North Pole.
* Velocity (v): This is the velocity of the object relative to the rotating frame of reference. For example, if an object is moving eastward, its velocity vector will point east.
* Cross Product: The "×" symbol represents the cross product between two vectors. The cross product results in a vector that is perpendicular to both input vectors.
Direction:
The direction of the Coriolis acceleration is always perpendicular to both the angular velocity vector (Ω) and the velocity vector (v). This means:
* In the Northern Hemisphere, the Coriolis acceleration deflects objects to the right of their motion.
* In the Southern Hemisphere, the Coriolis acceleration deflects objects to the left of their motion.
Magnitude:
The magnitude of the Coriolis acceleration depends on the latitude (φ), the object's velocity (v), and Earth's angular velocity (Ω):
|ac| = 2Ωv sin(φ)
* Latitude (φ): The Coriolis acceleration is strongest at the poles (φ = 90°) and weakest at the equator (φ = 0°).
* Velocity (v): The higher the velocity, the stronger the Coriolis acceleration.
Applications:
The Coriolis acceleration is responsible for several phenomena, including:
* The deflection of winds and ocean currents: This is why hurricanes rotate counterclockwise in the Northern Hemisphere and clockwise in the Southern Hemisphere.
* The rotation of weather systems: This includes the formation of cyclones and anticyclones.
* The deflection of projectiles and missiles: This is especially important for long-range artillery and rockets.
Note:
The Coriolis effect is a subtle force, but it has significant implications for large-scale phenomena like weather patterns and ocean currents.
